Iain Duncan Smith has joined political colleagues across the globe to wish the prime minister "a full and speedy recovery" following his recent heart scare.
Irish prime minister Bertie Ahern has sent a personal message
The Tory leader said his thoughts went out to the family of Tony Blair, who was back behind his desk at Downing Street on Monday, just 24 hours after he sought hospital treatment for an irregular heartbeat.
"His family will be feeling it a bit today, and anyone who has a family knows what it's like. Therefore my thoughts go to them as well," said Mr Duncan Smith.
"I hope the prime minister has a full and speedy recovery and everything is settled again."
Condoleeza Rice, the US National Security Advisor, told reporters travelling with President George W Bush in Thailand that the US administration was "very glad to hear" Mr Blair "is doing well".
The two leaders have not spoken since Blair's heart scare.
Irish leader Bertie Ahern has sent personal best wishes to his British counterpart, according to the Irish Embassy.
Get well messages
Foreign Secretary Jack Straw, who visited Mr Blair on Monday, told MPs in the House of Commons he was in "very good form and fully recovered from yesterday".
Shadow chancellor Michael Howard told BBC Radio 4's Today programme: "On behalf of every Member of Parliament, we all wish the prime minister a very full and very speedy recovery."
Ruth Kelly, financial secretary to the Treasury, told the programme: "I am obviously delighted, as is every member of the government and all MPs, that he now seems to be fully recovered."
Mr Prescott made a short visit to Number 10
John Burton, who runs Mr Blair's office in Sedgefield, said: "We have already had a lot of phone calls from local people wishing him well."
Mr Burton, the prime minister's Labour Party agent, added: "I have spoken to Cherie and Tony is fine. We are close family friends, we just asked after Tony. We were talking about him as just Tony not as the prime minister."
At Sedgefield Labour Club, regulars said they were thinking about Mr Blair.
Eric Wilkes, of the club's committee, said: "People were concerned. Everybody's thoughts are with him."
Deputy Prime Minister John Prescott made a short visit to Downing Street at lunchtime on Monday, but entered and left Number 10 without talking to reporters.
Shortly before his arrival, a basket of mixed flowers and four bouquets were delivered to the door, although it was unclear who had sent them.
Former Health Secretary Alan Milburn, a close friend of Mr Blair, arrived a little while later, but he entered Number 10 without commenting.
Meanwhile, Scottish National Party leader John Swinney sent the Labour leader his "very best wishes" and those of the SNP.
Mr Swinney, shadow first minister of the Scottish Parliament, said: "I was heartened to hear that he was only in hospital for a very short time and can only hope that he will be returned to full health swiftly."