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Mr Zelensky is in Vilnius for the summit[/caption]
After President Volodymyr Zelensky criticized the "absurd" delay to entrance, NATO states declared Ukraine can join the military alliance "when allies agree and conditions are met."
In a communique, Nato said it recognised the need to move faster but would not be drawn on a timeframe.
Earlier Mr Zelensky said there seemed to be "no readiness" to invite Ukraine to Nato or make it a member.
He is now in the Lithuanian capital Vilnius, where the summit is happening.
Kyiv accepts it cannot join Nato while it is at war with Russia but wants to join as soon as possible after fighting ends.
At a briefing on Tuesday afternoon Nato chief Jens Stoltenberg said allies had reaffirmed that Ukraine would become a Nato member and had agreed to drop the procedural need for a formal membership action plan.
"This will change Ukraine's membership path from a two-step process to a one-step process," he said.
But Mr Zelensky tweeted that the lack of an agreed timeframe meant his country's eventual membership could become a bargaining chip.
"A window of opportunity is being left to bargain Ukraine's membership in Nato in negotiations with Russia. Uncertainty is weakness," he said.
His comments follow disagreement between Nato members on Ukrainian membership.
Some fear near-automatic membership for Ukraine would give Russia an incentive to both escalate and prolong the war resulting from its full-scale invasion of its southern neighbour.
In its communique, Nato said Ukraine had become "increasingly interoperable and politically integrated with the alliance" and had also made progress on reform. Member states would support further reform, it said.
Mr Stoltenberg will meet Mr Zelensky at the inaugural meeting of the Nato-Ukraine Council on Wednesday.
The summit comes a day after Turkey dropped its opposition to Sweden joining the military alliance.
Turkey had previously spent months blocking Sweden's application, accusing it of hosting Kurdish militants. The country will now become the alliance's 32nd member after Finland - which borders Russia, joined in April.
Both countries announced their intention to join Nato after Russia invaded Ukraine.
A series of military packages for Ukraine were also announced at the summit on Tuesday.
A coalition of 11 nations will start training Ukrainian pilots to fly US-made F-16 fighter jets at a centre to be set up in Romania in August, officials said.
In May the US gave the go-ahead for its Western allies to supply Ukraine with advanced jets, including the long sought F-16s - a significant upgrade on the Soviet-era planes it is currently using.
Ukraine had repeatedly lobbied its Western allies to provide jets to help with its recently-begun counter-offensive aiming to retake territory seized by Russia.
However experts say the training of Ukrainian pilots to fly and operate Western jets will take some time.
Meanwhile Russian defence minister Sergei Shoigu was quoted by Russian news agencies as saying that Moscow would be forced to use "similar" weapons if the US supplied controversial cluster munitions to Ukraine.
The weapons release bomblets over a wide area and are banned by more than 100 countries over their impact on civilians.
Mr Shoigu said Russia had similar cluster weapons but had so far refrained from using them.
Rights groups say Russia and Ukraine have already used cluster munitions during the 17 months of war since Russia invaded last February.