BRUSSELS (Reuters) - NATO foreign ministers agreed Thursday to resume high-level formal ties with Russia, suspended last year after Moscow's military thrust into Georgia.

Russia immediately welcomed the move. This decision is a step in the right direction, Russia's RIA news agency quoted a foreign ministry spokesman as saying.

NATO Secretary General Jaap de Hoop Scheffer announced the decision after Lithuania dropped its objections to work resuming within the NATO-Russia Council, the body that directs cooperation between the two sides on security issues.

The ministers reached agreement to formally resume the NATO-Russia Council including at ministerial level ... as soon as possible after the NATO April summit, said de Hoop Scheffer.

Russia is a global player. Not talking to them is not an option, he added.

Earlier U.S. Secretary of State Hillary Clinton, attending her first NATO summit, pressed for a fresh start to relations with Moscow.

But she said the door to alliance membership must be kept open for ex-Soviet Georgia and Ukraine. Moscow strongly opposes their membership of the U.S.-led military alliance.

We can and must find ways to work constructively with Russia where we share areas of common interest, including helping the people of Afghanistan, said Clinton.

The Bush administration led the suspension of formal dialogue in the joint council.

Clinton is set to hold her first substantive talks with Russia's Foreign Minister Sergei Lavrov in Geneva Friday and agreement on resuming ties will help the atmosphere in that encounter.

The agreement of all 26 allies was needed and diplomats said Lithuania blocked a deal in a first round of talks on the issue.

A senior U.S. official said the Baltic country had wanted more discussions at the April 3-4 NATO summit whereas others thought it was not a good idea to hold back despite doubts about Russia.

Clinton and other allies emphasized that differences persisted with Russia, particularly over Georgia. But she said NATO had to find ways to manage these differences while also standing up for its principles when security or other interests were at stake.

We should continue to open NATO's door to European countries such as Georgia and Ukraine and help them meet NATO standards, Clinton said.

British Foreign Secretary David Miliband said that reviving formal NATO-Russia ties now was the way to deal directly with concerns.

(Additional reporting by David Brunnstrom; writing by David Brunnstrom and Sue Pleming; editing by Richard Balmforth)

Afghanistan Ukraine U.S. Hillary Clinton