Regarding the conversation relayed by the Turkish presidential spokesman Kalin; there are actually 6 issues. Apparently Russia sees agreement on the 4 bullets listed in CDJB's answer as preconditions for discussing the final two points:
"The first is Ukraine's neutrality," Kalin said in an interview with the Turkish newspaper Hurriyet published Saturday, adding that would mean Ukraine agreeing to not become a NATO member. "Second, disarmament and mutual security guarantees in the context of the Austrian model. Third, the process that the Russian side refers to as 'de-Nazification.' Fourth, removing obstacles to the widespread use of Russian language in Ukraine. It is understood that some progress has been made in the first four articles of the ongoing negotiations. It is too early to say that there is full agreement or that an agreement is about to be signed."
Kalin said Putin had additional demands that were "the most difficult issues" -- the recognition of the annexation of Crimea and the two so-called republics in Donbas. Kalin said these final two issues "are not acceptable demands for Ukraine and the international community."
"If a point is reached in the first four articles and an agreement is reached, there can be a discussion at the leaders' level regarding the fifth and sixth articles," Kalin said in the interview, adding that if the negotiations take place, "it may be possible to reach an agreement and end the war."
I think people have interpreted that in various way, e.g. that Russia might be flexible on points 5 and 6... or that that it is what it really wants.
Earlier, on March 7, roughly the same list of demands had been issued by the Kremlin more directly (and without any "algorithm" for negotiations); notably this also included Crimea and the Donbass republics:
Russia has told Ukraine it is ready to halt military operations "in a moment" if Kyiv meets a list of conditions, the Kremlin spokesman said on Monday.
Dmitry Peskov said Moscow was demanding that Ukraine cease military action, change its constitution to enshrine neutrality, acknowledge Crimea as Russian territory, and recognise the separatist republics of Donetsk and Lugansk as independent states.
It was the most explicit Russian statement so far of the terms it wants to impose on Ukraine to halt what it calls its "special military operation" [...]
I'll add something that Putin only explained later in his speech on March 16: why attack Kyiv instead of just limiting operations to the Donbass:
I would like to emphasise this point and draw your attention to it: if our troops had acted only within the people's republics and helped them liberate their territory, it would not have been a final solution, it would not have led to peace and would not have ultimately removed the threat – to our country, this time to Russia. On the contrary, a new frontline would have been extended around Donbass and its borders, and shelling and provocations would have continued. In other words, this armed conflict would have continued indefinitely. It would have been fuelled by the revanchist hysteria of the Kiev regime, as NATO deployed its military infrastructure faster and more aggressively. In this case, we would have been faced with the fact that the attack, the offensive weapons of the alliance were already at our borders.
I will repeat – we had no alternative for self-defence, for ensuring Russia's security, to this special military operation. [...]
Also, this speech repeated the claim that Ukraine was preparing to acquire nuclear weapons; that had been raised earlier by other Russian officials, but Putin also included it in that speech:
Moreover, the Kiev authorities also announced their intention to have nuclear weapons and delivery vehicles. This was a real threat. With foreign technical support, the pro-Nazi Kiev regime would have obtained weapons of mass destruction in the foreseeable future and, of course, would have targeted them against Russia.
And something fairly similar about biological weapons:
[...] we have grounds to assume that components of biological weapons were being created in direct proximity to Russia on the territory of Ukraine.
Our numerous warnings that such developments posed a direct threat to the security of Russia were rejected with open and cynical arrogance by Ukraine and its US and NATO patrons.
In other words, all our diplomatic efforts were fully in vain. We have been left with no peaceful alternative to settle the problems that developed through no fault of ours. In this situation, we were forced to begin this special military operation.
It's not clear however what this means (if anything) in terms of concrete objectives, since the international community (e.g. UN representatives) said they don't know anything about those alleged programs (of either kind). So if Russia seemingly makes an objective in dismantling them as part of Ukraine's demilitarization, it's rather unclear what Ukraine would have to do to comply. I think no concrete details about what the demilitarization means in the Russian view have been made explicit, but this is the closest thing I've heard raised.
It's also worthwhile mentioning that the Kremlin not being incredibly clear about their objectives may have been part of their PR strategy, so e.g. that may claim victory on wider range of outcomes on the ground. No much later after I wrote the above, on March 25 news was that they they've declared to re-focus on the Donbass, which was now described as the "main goal":
In a scaled-back formulation of its war goals, Russia said on Friday that the first phase of its military operation was mostly complete and it would focus on completely "liberating" Ukraine's breakaway eastern Donbass region.
The announcement appeared to indicate that Moscow may be switching to more limited objectives after running into fierce Ukrainian resistance in a month of war.
The defence ministry said Russian-backed separatists now controlled 93% of Ukraine's Luhansk region and 54% of the Donetsk region. They jointly make up the Donbass.
"The main objectives of the first stage of the operation have generally been accomplished," Sergei Rudskoi, head of the Russian General Staff's Main Operational Directorate, said in a speech.
"The combat potential of the Armed Forces of Ukraine has been considerably reduced, which ... makes it possible to focus our core efforts on achieving the main goal, the liberation of Donbass."
A senior diplomatic source in Moscow described it as a face-saving move and possible prelude to a climb-down by Russia. [...]
Rudskoi said Russia's military had considered confining its operation just to Donbass but opted for extending across Ukraine to damage its military infrastructure and tie down forces so as to prevent them reinforcing the east.
Russia did not rule out storming cities, he said, but as its military completed tasks "our forces and resources will be concentrated on the main thing - the complete liberation of Donbass."
