The Chief Secretary to the Treasury made clear the Lib Dems would accept nothing short of another coalition if there is a hung parliament at the next general election.
His comments come just days after reports Labour was prepared to keep Nick Clegg as Deputy Prime Minister if it ensured Ed Miliband entered Downing Street.
Mr Alexander's party's stance does not in itself prevent Labour or the Conservatives attempting to rule as a minority government.
But it does suggest such a task could be more difficult.
It appears to rule out arrangements such as 'confidence and supply' - in which a smaller party offers support on the government's budget and other issues, but does not enter into a formal coalition. Mr Alexander said that the scale of the challenge that still faces the UK economy meant such measures would not be in the "national interest".
A minority government, he said, "would not have the strength and stability that we need to ensure that as a country we continue to make the progress economically that we have over the last four years".
He added: "Of course there are differences with Labour on the economy and the Conservatives on Europe, but the whole point of negotiating a coalition is to try to find a way to bridge those differences and make sure we can keep the country on the right tracks."
Mr Alexander also failed to rule out speculation that he wants to lead his party.
He said: "Nick Clegg and I have been close friends and strong allies since I helped run his leadership campaign. I will cross that bridge if it comes."