Qazi Hussain Ahmed, head of the right-wing Jamaat-e-Islami party, told a news conference any softening of Pakistan's stand on these three issues would be met with strong resistance.
Musharraf, a key ally of the United States in its war against terror, is locked in a bitter dispute with a coalition of Islamist opposition parties over his extensive powers, and dual role as president and commander in chief of the armed forces.
"He (Musharraf) has expressed a soft corner toward Israel recently," said Ahmed. "If there is any talk on recognising Israel, we will vigorously struggle to remove Musharraf from power."
Ahmed threatened to launch what he called a nationwide agitation should Musharraf yield to any American pressure on Pakistan's nuclear arsenal or accepted a formula for the resolution of the dispute over divided Kashmir, over which Pakistan and India have fought two wars.
"Musharraf does not need to win the confidence of foreigners, he needs to win the confidence of his own people," Ahmed added.
The Islamist coalition has angered moderates and drew comparisons with Afghanistan's former Taliban regime this month when they voted to impose Islamic sharia law in North West Frontier Province.
Musharraf, who is on a four-nation tour that takes him to Washington, said on Tuesday in London the government was succeeding in cracking down on extremism.
He told Reuters earlier this week the majority of Pakistanis were against Talibanisation.
"The issue is the vast majority is being held to ransom by a small minority, so I think one needs to set the record straight. One needs to be proactive in talking about Islam and what we want," he added.
Musharraf, who says he stands for a moderate, progressive Islamic Pakistan, became a key ally in the US war on terror when he abandoned the Taliban in neighbouring Afghanistan in the wake of the September 11, 2001, attacks.