Mr Straw has had to cut short his foreign trips
His 84-year-old father was taken ill while Mr Straw was holding talks in India with the Foreign Minister Jaswant Singh.
Mr Straw was flying back to the UK on Wednesday.
He was set to attend the Commonwealth Heads of Government Meeting (CHOGM) alongside Prime Minister Tony Blair in Queensland at the end of the week.
But now Baroness Amos, one of his ministers, will represent him at CHOGM in his absence.
'Terrorism is terrorism'
Earlier in Delhi, Mr Straw told a press conference that terrorism must end before India and Pakistan can resolve their differences through dialogue.
He insisted those responsible for the attack on the Indian parliament in December be brought to justice.
India blames the attack on Pakistani-based militants.
Referring to the parliament attack, Mr Straw said: "We view the matter as seriously as thought the attack... could have been an attack on the British parliament.
"Terrorism is terrorism wherever it occurs," he said.
Referring to India and Pakistan's dispute over Kashmir, the foreign secretary added: "Support for terrorism has to stop for a meaningful dialogue to begin."
Pakistan's President Musharraf in January promised to punish anyone responsible for militant activity against India in Kashmir.
No details
But he is refusing to hand over those on a list of 20 people India wants extradited to face the courts in India.
Fourteen people died in the attack on the Indian parliament. The incident led to both sides massing troops on their common border.
Mr Straw also held talks with the leader of Afghanistan's interim government, Hamid Karzai, who is also in Delhi.
Mr Straw said the two men had discussed an extension of the United Nations mandate for the international peacekeeping force in Afghanistan.
He did not give details.
Mr Karzai wants an expanded role for the force, both in terms of time scale and the areas it covers.
Difficult balance
Its mandate expires in July, but many in Kabul say it will take much longer than that before an Afghan force can be established and ready to take control.
Mr Straw has said he would consider backing an extension, which would have to be approved by the United Nations, but it is far less likely that Britain would want to extend its own leadership role.
At the moment, the multi-national force only operates within Kabul and Afghan leaders now want a larger force which could also cover other key areas.
A BBC correspondent in Delhi says that for the international community, it is a difficult balance between their commitment to ensuring stability for the new Afghanistan and concerns about the political cost and risk to personnel of a larger and longer-term involvement.