Russia strongly opposed the plans, fearing they would neutralise its own nuclear arsenal.
The new scheme unveiled by Barack Obama, the US president, envisages the deployment first of sea-based interceptors and then of land-based systems, including the proposed system in Poland.
"Poland finds the new anti-missile project as very interesting and important and, in the appropriate scale, we are ready to participate," Tusk said.
Biden, on the first leg of a European visit, said that the new system would be more effective and would cover a much greater part of European territory than the previous plan which was instigated by George Bush, the former US president.
"I welcome the prime minister's declaration that Poland stands ready to host elements of missile defence," he said.
Raising concerns in Poland and other former Soviet satellites, Obama has made "resetting" relations with Russia a major foreign policy objective in order to obtain Moscow's co-operation on Iran, Afghanistan and other strategic issues.
Russia has welcomed his decision to shelve the Bush missile shield plan, which Moscow had regarded as a direct threat to its own security.
Biden sought to reassure Poles that the Obama administration would not strike any deals with Russia affecting their security over their heads.
"Our commitment to Poland is unwavering," he said.
For Warsaw, which is perturbed by Russia's more assertive foreign and security policy, the type of anti-missile system is less important than a clear US commitment to its security.
Poland, which joined Nato a decade ago, has long complained that it hosts no US troops or major military installations despite a track record of sending troops to help in US-led missions in Iraq and Afghanistan.
"We do not care so much about the hardware, but about the perception that the security status of this region is equal to that of western Europe," said Witold Waszczykowski, deputy head of Poland's National Security Bureau.
Tusk and Biden did not make any reference to plans to deploy a Patriot missile battery in Poland, which diplomats said indicated that talks on the legal and technical aspects of the plan were still ongoing.
|Biden laid a wreath at the monument to victims of the Warsaw ghetto uprising [EPA]
Under a deal negotiated with the Bush administration in parallel with the missile shield plan, Poland secured a commitment that the US would send an armed Patriot battery to Poland from Germany several times each year until 2012 to help upgrade Polish air defences.
Earlier, Biden laid a wreath at the monument to victims of the Warsaw ghetto uprising, murdered by the Nazis during the second world war, and met leaders of Warsaw's Jewish community.
The vice-president also held talks with Lech Kaczynski, Poland's president, a conservative known for his anti-Russian rhetoric and a strong supporter of the previous Bush shield plan.
Biden will leave for Romania later on Wednesday.