Speaking at a joint news conference in Delhi with his Indian counterpart Jaswant Singh, Mr Straw said the stand-off between India and Pakistan had "obvious implications" for the rest of the world.
Mr Singh said General Musharraf had been given enough time to stop attacks and that it was "vital that he sees the urgency of the situation".
The British foreign secretary is meeting Indian leaders a day after he held talks with General Musharraf to try to avert a possible war between the two nuclear powers.
Mr Straw's mission comes amid increasing tension as fighting continued across the Kashmiri border and Pakistan test-fired a missile capable of carrying nuclear warheads for the third time on Tuesday.
Authorities in Pakistan said at least five people were killed overnight and eight others injured when Indian troops shelled the Pakistani border village of Bajra Gahri in Punjab province.
The Indian army said at least six people were killed in cross-border firing in Dras, 150 kilometres (155 miles) north of Srinigar, the summer capital of Kashmir.
Concrete steps
Kashmir conflict:
Asked whether General Musharraf was genuine in his commitment to halt cross-border attacks, Mr Straw said he believed the president was serious "but the test of everything is action on the ground".
The foreign minister said the international community "looks to press Musharraf to assure that this undertaking is fulfilled on the ground".
Earlier, Mr Straw told reporters that he had assured India that Britain condemned terrorism "in all its forms, including cross-border terrorism and terrorism that is dressed up as 'freedom fighters'".
The foreign secretary is due to hold talks with Indian Prime Minister Atal Bihari Vajpayee later on Wednesday.
Indian impatience
Indian Foreign Minister Jaswant Singh said at Wednesday news conference that General Musharraf "has had all the time that he wants since 11 September" to crack down on extremist groups.
He said India had "waited patiently" for Mr Musharraf to stop Pakistan-based militants crossing the border into Indian-administered Kashmir.
India:
Pakistan:
Mr Singh said there were various proposals to monitor whether Mr Musharraf was delivering on his promises to halt attacks.
In a speech on Monday, the president said infiltrations into Indian-administered Kashmir had stopped.
But, Mr Singh on Tuesday described the speech as "belligerent posturing", adding that "tensions have been added not reduced".
But he again ruled out India launching the first nuclear strike in any conflict.
India began the military build-up after an attack on its federal parliament in Delhi last December.
Tension rose again two weeks ago after an attack on an Indian army base in Kashmir in which more than 30 people died.
With both sides on the brink of war, Pakistan said it was sending special envoys abroad to explain Pakistan's position in the crisis.