By Robin Emmott and Philip Blenkinsop

BRUSSELS (Reuters) - NATO's chief said on Tuesday that Russia's seizure of Crimea remained a major sticking point, sounding a note of caution a day after U.S. president-elect Donald Trump agreed to boost cooperation with Russian President Vladimir Putin.

The U.S.-led military alliance wanted to keep talking to Moscow, NATO Secretary-General Jens Stoltenberg said before talks with EU defense ministers in Brussels.

But Russia's 2014 annexation of Crimea was an unacceptable breach of Ukraine's sovereignty, he added.

His message was echoed by German Defence Minister Ursula von der Leyen who said she was also concerned about Russia's military activities in eastern Ukraine and Syria. "It is ... important not to forget our principles," she added.

Germany and other European powers have said they are concerned about what Trump's election win will mean for the United States' commitment to NATO.

During campaign speeches, Trump had said Washington might not defend a NATO member who had not paid its contributions to the alliance and told ABC News in July he might recognize Crimea as Russian.

"The message from NATO has been that we want dialogue with Russia," said Stoltenberg, whose country Norway borders Russia.

"Russia is our biggest neighbor, Russia is there to stay and especially when tensions run high and especially when we face many different security challenges, it is important to have dialogue."

Stoltenberg said he hoped NATO envoys and Russia's ambassador to NATO, Alexander Grushko, could meet in the NATO-Russia Council soon.

But he said: "We will never respect or accept the violation of the territorial integrity and sovereignty of Ukraine."

The Kremlin says Crimea, where Moscow is building up its military presence, is Russian land and its status non-negotiable. In Putin's call with Trump both men agreed "to normalize relations and pursue constructive cooperation on the broadest possible range of issues," according to a statement from the Kremlin.

The United States and the European Union imposed sanctions on Russia over Crimea in July 2014 and then tightened them in December 2014, banning EU citizens from buying or financing companies in Crimea, whose annexation has prompted the worst East-West stand-off since the Cold War.

Russia hopes the United States under Trump will repeal those measures, potentially pressuring the European Union to do the same.

Von der Leyen described the annexation of Crimea as "an open point".

"We should also not forget that Russia bears a humanitarian responsibility in Aleppo, where 250,000 people are threatened with death from hunger," she added, referring to the northern Syrian city where Russian air strikes are backing government forces against rebels.

(Reporting by Robin Emmott and Philip Blenkinsop; Editing by Andrew Heavens)