NATO Secretary-General Anders Fogh Rasmussen has said that Russia is withdrawing around two-thirds of the troops it had near the Ukrainian border.
Rasmussen, speaking to Reuters on the sidelines of a meeting of the NATO Parliamentary Assembly in the Lithuanian capital, Vilnius, on May 30, said there are "signs of at least a partial withdrawal."
The estimate is far higher than previous estimates made by NATO of the extent of a Russian withdrawal, which Russia has pledged a number of times, most recently this week.
Rasmussen also said that NATO and Russia would meet in the framework of a cooperative body, the NATO-Russia Council, on June 2 but gave no further details.
Earlier, Ukraine's government said it will press on with an offensive to restore peace and order in the separatist-controlled east, as a second team of OSCE monitors was detained by pro-Russian gunmen in the region.
Acting Defense Minister Mykhaylo Koval said government forces have "completely cleared" pro-Russian rebels from parts of the separatist east.
Koval was speaking to reporters in Kyiv on May 30, one day after at least 12 government troops, including a general, were killed when rebels shot down an army helicopter.
"Our armed forces have completed their assigned missions and completely cleared the southern and western parts of the Donetsk region and the northern part of the Luhansk region from the separatists," Koval said.
"Our given task is to bring peace and order to the region," he added.
Koval also repeated charges that Russia was carrying out "special operations" in eastern Ukraine.
He said Ukrainian forces would continue with military operations in border areas "until these regions begin to live normally, until there is peace."
Meanwhile, the Organization for Security and Cooperation in Europe (OSCE), the pan-European rights and security body, said a team of four international monitors and a Ukrainian language assistant was stopped by gunmen in the town of Severodonetsk, 100 kilometers north of Luhansk.
The OSCE said it lost contact with the team late on May 29.
It said the detained team is in addition to another group of monitors still missing in eastern Ukraine, which was last heard from on May 26.
The OSCE says members of that team -- Danish, Turkish, Swiss, and Estonian nationals -- were on a routine patrol east of Donetsk.
A rebel leader confirmed on May 29 that those four monitors were in their custody. The rebels assured journalists that they would "deal with this and then release them" but did not give a specific time frame.
The OSCE teams are in Ukraine to monitor the security situation following the rise of a pro-Russia separatist insurgency.
In a separate development, one faction of pro-Russian insurgents in eastern Ukraine has reportedly evicted another faction from the regional administration building in Donetsk, which has served as the separatists' headquarters.
Western media reports said heavily armed fighters of the so-called Vostok Battalion flooded into Donetsk last weekend.
Many are believed to be from Chechnya and other areas in the Caucasus.
The U.S. State Department said on May 29 that U.S. Secretary of State John Kerry had raised concerns about foreign fighters entering Ukraine -- particularly Chechens -- with Russian Foreign Minister Sergei Lavrov.
With reporting by Reuters, AFP, AP, and Interfax