Basescu insisted that the project is in his country's interest and is not directed against Russia.
"The new system is not directed against Russia. I repeat: Romania is not hosting a system directed against Russia, but against other threats," Basescu stated.
He added that the old US missile defence system based in Poland and the Czech Republic covered only part of Romania, whereas now the country's entire territory would be protected.
Basescu said the request had been made by Ellen Taucher, Under-Secretary of State for Arms Control, who is heading a delegation of US experts in Romania.
Basescu also insisted that the step-by-step development of a missile shield in Europe is consistent with decisions taken at the 2008 NATO summit in Bucharest and the alliance's 2009 summit, held in Kehl and Stasbourg.
He explained that Romania would host land-based anti-missile rockets and that the system would be operational by 2015.
The decision to install part of the US missile shield on Romanian territory appears to have won the approval of the opposition Social Democrats (PSD).
Mircea Geoana, PSD leader, described the plan as a "logical" consequence of the changed plans over the location of the shield, adding that it is "related to national security and the North Atlantic area".
Teodor Melescanu, from the liberal party PNL, who is also president of the Senate's defence committee, said he was convinced that Russia would also be involved in the project.
MEP Ioan Mircea Pascu (S&D), a former defence minister, said that he expected Russia to react negatively to the announcement. He added, however, that he believed a previous consultation between Washington and Moscow had taken place.
Unlike some other EU countries, popular support for US military policy is very high in Romania, Reuters reports. Romania already hosts a small US base and training facilities, part of a Pentagon shift from large Cold War-era centres in Western Europe towards smaller installations nearer hot spots such as the Middle East.