Member of Hizb Allah's political bureau Ali Fayadh on Wednesday said President Bush's call was an interference in Lebanon's internal affairs, reported Aljazeera.
Fayadh was quoted by Aljazeera as saying that the Hizb Allah rejected Bush's call to give up its arms as it was necessary to counter the continuous Israeli threats against Lebanon.
However, speaking to Al-Arabiya satellite television, a member of Hizb Allah's political bureau, Nawaf Musawi, said that in line with a European change towards his organisation, Bush was "trying to propose an approach different from the traditional American approach towards Hizb Allah".
The United States has long condemned Hizb Allah, but on Tuesday Bush said the Iranian-backed group could shed its "terrorist" label and win US recognition if it disarms and stays out of the Israeli-Palestinian dispute.
Hizb Allah draws support from
Lebanon's Shia community
"We view Hizb Allah as a terrorist organisation," Bush said. "I would hope that Hizb Allah would prove that they are not by laying down arms and not threatening peace."
Hizb Allah's media office declined to comment on Wednesday, but Musawi said: "We read the (Bush) stand in a good way, but also read it in the light of Israeli influence on US policy."
The media office said Hizb Allah's leader, Shaikh Hasan Nasr Allah, would probably address Bush's remarks in a Wednesday night interview on the group's Al-Manar television.
Hizb Allah has repeatedly spurned calls to disarm. Its deputy leader, Shaikh Naim Qasim, said last week the group would not disarm as long as the Palestinian-Israeli conflict persists and poses a threat to Lebanese security.
Hizb Allah, which draws its support from Lebanon's 1.2 million Shia community, is widely admired in the country and the Arab world for its military role in forcing Israel to leave southern Lebanon in 2000 after an 18-year occupation.
In the past month, Hizb Allah has demonstrated its political influence by organising two huge rallies in support of Syria's military presence in Lebanon.
On Tuesday, Hizb Allah supporters took part in an anti-US protest of several thousand people outside the American Embassy in Beirut.
Bush is "trying to propose an approach different from the traditional American approach towards
Hizb Allah political bureau
At the same time, there have been calls for Washington to support moves to nudge Hizb Allah into mainstream political life in Lebanon as Washington pushes for an end to Syrian influence there.
The US and many other Western nations have linked Hizb Allah to the pro-Iranian group that carried out bombings of the US embassy and US Marine base, killing about 270 Americans, during the 1980s.
Hizb Allah was also widely blamed for the kidnapping of Americans in Beirut during the 1975-90 civil war. Hizb Allah denies links to the group and the kidnappings.