Lawyer Alyza Lewin confirmed she had filed a suit in federal court on behalf of Ari and Naomi Zivotofsky.
As parents of an 11-month-old boy born in Jerusalem, the couple say they want Israel named on his passport and birth certificate.
"They were told, 'We can't do that,'" said Lewin, who explained: "The country place on the passport and on the birth certificate is blank."
Her clients' suit is based on a US law adopted in 2002 by Congress, the Israeli Capital Recognition Act, which stipulates that the State Department must mention Israel when the birthplace is Jerusalem.
The al-Aqsa Mosque was the scene
of Prophet Muhammad's
"The odds are good," said Lewin.
However Washington-based Nihad Awad, executive director of the Council on American-Islamic Relations, said the legal action went "against all norms".
He told Aljazeera.net: "You can not impose this will on the international community without the agreement of the Palestinians.
"This goes against institutional common sense," he added saying the status of Jerusalem was a hotly disputed issue between Palestine and Israel.
Earlier this month there was international outrage across the Muslim world when Aljazeera.net revealed that a UK-based publisher referred to Jerusalem as the capital of Israel in a newly published atlas.
Jerusalem is the third holiest site in the world for Muslims, and the scene of the Prophet Muhammad's night journey to the al-Aqsa mosque.
Massoud Shajareh of Britain's Islamic Human Rights Commission demanded an apology from publisher Harper Collins after the error was spotted in its new mini atlas.
He said: "They are saying something that is untrue and contrary to international law. It is legitimising the Israeli occupation of Palestine."
The United Nations Resolution 181 of 1947 on the partition of Palestine foresaw Jerusalem as a "corpus seperatum" in which the holy city would be placed under international custodianship.
The resolution was accepted by representatives of what would become the Jewish state, but was rejected en bloc by Arab nations.
After the state of Israel was created in May 1948, the first Israeli-Arab conflict concluded with Jerusalem's partition into two sectors: the western one, to be Jewish, and the eastern one under the control of Jordan.
In December 1949, the Israeli parliament declared West Jerusalem the capital of the state of Israel contrary to the US position. Even today the US refers to Tel Aviv as the Israeli capital.
During the Six-Year War of June 1967, Israel annexed West Jerusalem. And in July 1980, the Knesset voted to proclaim in its Basic Law, "Jerusalem, complete and united, is the capital of Israel."
UN Resolution 672 of October 1990 calls East Jerusalem illegally occupied territory.
Almost all of the embassies in Israel are based in Tel-Aviv and the vast majority of the world will only accept Tel-Aviv as the capital apart from El Salvador and Costa Rica.
The status of Jerusalem is such a highly sensitive issue that it has stalled peace negotiations on many occasions between Palestinians and Israelis.