Two of the US administration's top officials are holding talks in Europe aimed in part at drumming up support for operations in Iraq.
US troops make up the majority of foreign forces fighting in Iraq
Defence Secretary Donald Rumsfeld is in the French city of Nice to call for Nato colleagues to do more for the military effort there.
Secretary of State Condoleezza Rice is in Brussels for talks with Nato and the European Union.
The US-led invasion of Iraq during the first Bush term badly strained ties.
Some Nato countries, notably France and Germany, said they would have nothing to do with operations in Iraq. Spain initially sent troops but then decided to pull them out.
When Mr Rumsfeld meets his fellow defence ministers in Nice, he will try to persuade more doubtful Nato members to contribute troops to a mission in Iraq to train officers for the local armed forces.
Rumsfeld visits France a day after Condoleezza Rice
The training mission should number 300 personnel from Nato countries but there are fewer than 100 on the ground so far.
UK Prime Minister Tony Blair is apparently convinced that the final arrangements for the training will be made at a Nato summit scheduled for 22 February in Brussels, the BBC's defence and security correspondent, Paul Welsh, reports.
In Nice, Nato members Spain and Lithuania may also agree to lead new operations in the west of Afghanistan, where a Nato-led force has long been in place.
The BBC's Pentagon correspondent, Adam Brookes, says Mr Rumsfeld will certainly not be making any apologies for Iraq, but the very fact he is going to France - a country much vilified in Washington over the last two years - sets a conciliatory tone.
Ms Rice will meet Nato foreign ministers in Brussels as part of preparations for President George W Bush's attendance at the summit.
RICE'S SEVEN-DAY TOUR
Fri: Met UK's Tony Blair and Foreign Secretary Jack Straw in London; talks with Germany's Gerhard Schroeder in Berlin
Sat: Talks with leaders in Germany, Poland and Turkey; met Russian foreign minister in Ankara
Sun: Met Turkish government, then on to Israel to meet Ariel Sharon
Mon: Talked with Mahmoud Abbas in West Bank
Tue: Met with Italian counterpart in Rome, then on to Paris to deliver speech
Wed: Talks with French ministers, then on to meet Nato and EU officials in Brussels and Luxembourg
Thurs: Returns to Washington
Nato chief Jaap de Hoop Scheffer said he expected progress from the talks, as well as the Bush summit.
"Transatlantic relations are not only something you talk about, it's also something you do," he said.
Ms Rice's meeting with EU officials is expected to touch on EU plan to lift an embargo on arms sales to China - a plan which the US deplores, says the BBC's Europe correspondent, Tim Franks.
There is also friction over Iran's alleged nuclear arms plans, and the Kyoto protocol on global warming.
Ms Rice is nearing the end of a tour that has focused on reviving relations between the US and Europe.
In Paris on Tuesday, she used her first key foreign policy speech to call for a "new chapter" for Nato.
"It is time to turn away from the disagreements of the past," she said, adding that Europe must "stand ready to work with America".
French Foreign Minister Michel Barnier welcomed the top US diplomat, saying Paris and Washington were "each other's oldest allies".
However, he added that "alliance doesn't mean allegiance".
Ms Rice will also visit the EU presidency in Luxembourg on Wednesday before returning to the US on Thursday.