Mr Tusk thinks Poland should be rewarded for hosting the shield

President George W Bush made the promise during talks with Polish Prime Minister Donald Tusk in Washington.

Before the meeting, Mr Tusk said the US anti-missile system, which has angered Russia, would reduce Poland's security.

Mr Bush says the shield will guard against possible attacks by "rogue states", such as Iran or North Korea.

"There is a commitment to a system that respects Poland's sovereignty and that will ensure that the people of Poland will not be subjected to any undue security risks," said Mr Bush after the meeting.

"We just want to assure people that [the missile defence shield] is necessary and at the same time there will be this modernisation effort that will take place", he added.

'Rogue state' defence

The US opened negotiations last year with the previous Polish government of Prime Minister Jaroslaw Kaczynski, a strong backer of the US proposals.

But Mr Tusk's government, which came to power in November, has argued that Poland should get some reward for allowing the US missiles to be based in the country.

It wants anti-aircraft missiles - such as the US Patriot, which was used to shoot down Iraqi Scud missiles in the 1991 Gulf War - in return.

The Americans know our expectations and their understanding of Polish expectations is slowly taking a very promising shape

Polish Prime Minister Donald Tusk

Russia's outgoing President Vladimir Putin has condemned the plans to include Poland and the neighbouring Czech Republic in its proposed missile shield.

An associated radar system could be based in the Czech Republic.

"The Americans know our expectations and their understanding of Polish expectations is slowly taking a very promising shape," Mr Tusk told Polish news agency PAP before flying to the US.

The two leaders are also thought to have discussed further Nato involvement in military missions in Afghanistan and Iraq.

Polish troops took part in the US-led invasion of Iraq in 2003, and a multinational division in the south of the country is commanded by Polish forces - though the Poles intend to withdraw their troops by October.

Mr Tusk is also expected to meet UN Secretary General Ban Ki-moon on Tuesday.