Before the hearing, one of the lawmakers on the Treasury Select Committee said Diamond was making a serious accusation.
"He has made allegations about the behavior of a very highly respected and trustworthy deputy governor of the Bank of England, Paul Tucker, and many of us will want to get to the truth of that," David Ruffley said.
The allegation "goes to the very heart of the integrity and probity of regulators in the City of London. One of those is the Bank of England," he said.
Tucker asked the committee Wednesday for a chance to testify, the panel said in a statement.
Diamond has long been a controversial figure and has been a vocal backer of huge bonuses for bankers.
"It's about pay for performance," he told CNN earlier this year, calling bonuses "rewards for success."
His own pay package remains "under discussion," Barclays told CNN on Wednesday.
Diamond's total compensation package for 2011 was worth £6.3 million ($9.8 million), including salary, bonuses and share options, the bank said.
The annual bonus consisted of £2.7 million ($4.2 million) in shares and was deferred over three years, the bank said.
The chairman of the Financial Services Authority, Britain's banking regulator, last month blasted the "cynical greed of traders asking their colleagues to falsify their Libor submissions so that they could make bigger profits."
Chairman Adair Turner said the scandal "has caused a huge blow to the reputation of the banking industry" and "has justifiably shocked and angered people."
At least seven other banks are under investigation on suspicion of rate-fixing, leading to speculation that Diamond could be the first of many executives to resign.
Financial regulators in London have not named the banks, but Deutsche Bank, Royal Bank of Scotland, Credit Suisse and UBS have acknowledged that they are under investigation.
Citigroup and JPMorgan Chase have also confirmed that they are under investigation.
Bank of America has refused to comment on reports that it is being probed.
British Prime Minister David Cameron said Monday that a full parliamentary inquiry would be held into the Libor rate-fixing scandal and standards in the banking industry, with witnesses called to give evidence under oath.
Barclay's is the 15th-largest bank in the world, according to an annual list of the world's top 1,000 banks released Monday by The Banker magazine.
It is Britain's second-most profitable bank, and the 18th-most profitable in the world, the trade magazine said.