David Cameron has urged the Royal Bank of Scotland to show "restraint" in its bonus packages for senior colleagues of chief executive Stephen Hester.
The Prime Minister said the remuneration arrangements put in place by the former Labour government for executives at the part-nationalised bank had to be followed.
But he added: "They have got to have proper regard in terms of restraint when they have had so much money from the taxpayer and they have made so many mistakes in the past."
Mr Cameron's comments come as a number of executives in RBS's investment branch are expected to be offered large payments in the coming weeks.
Under mounting pressure, Mr Hester gave up his offered £963,000 shares package bonus on Sunday night.
Mr Cameron said the "main thing" was to ensure that RBS was turned around to safeguard the taxpayers' investment.
He suggested the bank ought to explain better why it felt its executives were worth the bonuses they were being offered despite a falling share price.
"I think what needs to happen is a sense of restraint which is exactly what the Government urged on RBS in the first place, and they need to do a better job - as everybody has - about explaining how pay is linked to performance," he told a press conference in Brussels.
"And if performance isn't the share price then people need to see very clearly what it is you are doing to sort out that bank, to turn it round, to make it safe, to make sure its long-term value... because that's what I care about.
"Is the taxpayer going to get their money back, that we had to put into this bank that was so badly managed in the past?
"These are the things they have got to focus on."
The Prime Minister said the arms-length management arrangements for RBS, including the decision to run it as a commercial business, had been put in place by Labour.
He indicated the Government would look at those arrangements although it had no plans to change them.
"I think the main thing that needs to happen is for this bank to be turned round, for its balance sheet to be made safe and for taxpayers' money, vitally, to be recovered," he said.
"Of course we will look closely at the arrangements that were put in place. We don't plan to change them but we will look closely at them.
"But I think it's very important this bank operates under these arrangements."
Ministers including Chancellor George Osborne and Business Secretary Vince Cable welcomed Mr Hester's announcement that he was waiving his bonus.
But Sir Roger Carr, the president of the CBI, warned today that the "vilification" of Mr Hester would deter others from taking on "difficult tasks of national importance", adding: "This cannot be in the long-term public interest."
Writing in the Times, Sir Roger said: "The row has ignored the fact that a talented man with many opportunities for personal enrichment has chosen to accept a job that few were capable of doing and even fewer had the appetite to undertake."
Meanwhile, Labour leader Ed Miliband insisted Mr Hester's announcement would not draw a line under the issue of City pay.
Labour will use an opposition day debate in the Commons next Tuesday to urge Conservatives and Liberal Democrats to back a £2 billion tax on bankers' bonuses, which they say could fund the creation of 100,000 jobs elsewhere.
The party had initially planned to use next week's debate to force a vote calling for Mr Hester to be stripped of his bonus, and Mr Miliband said that it was this threat which persuaded the RBS boss to give up his bonus.
The Labour leader said: "The Government has dragged its feet, has nodded this bonus through, and I think we have seen that they have got a completely tin ear when it comes to understanding what people are feeling.
"I don't think this can be just a one-off episode, because if we don't deal with this systematically, if we don't deal with the issue of bankers' bonuses in a proper way, this kind of thing is just going to re-occur."
But Downing Street insisted that ministers would not be "micro-managing" RBS and that decisions on future bonuses at the 83% state-owned bank were a matter for the board.
Mr Hester was appointed chief executive at the end of 2008 to replace Sir Fred Goodwin, after the bank had to be bailed out by the Government.