Alliance is a small party which has lost votes in recent elections to other pro-Agreement politicians.
It has never held a Westminster seat.
Announcing the move on 2 April leader Sean Neeson said: "It is clear that the Agreement and its implementation are set to be major issues in the forthcoming general election.
" Some people are hellbent on turning it into a re-run of the referendum "
"Some people are hellbent on turning it into a re-run of the referendum."
Mr Neeson said his party would not now be contesting North Belfast, Upper Bann, Fermanagh and South Tyrone, Mid Ulster and Newry and Armagh.
He added that in each of these constituencies the party would ask its supporters to vote for the pro-Agreement candidate with the best chance of winning.
The party is still fighting ten of the eighteen seats.
"We are still considering our position in South Down and West Tyrone," said Mr Neeson.
"It is likely that the Alliance votes in many of these constituencies could affect the outcome."
Mr Neeson also called on the other parties to rise above narrow electoral objectives and look to the wider interests of the Agreement.
He has been critical of the SDLP and Ulster Unionist Party for pursuing their own electoral ambitions at the expense of what he sees as the greater interest of the pro-Agreement alliance.
He said: "The SDLP seem intent on running everywhere and maximising their own vote irrespective of the consequences for the agreement.
"The Ulster Unionists have made it clear that they wanted Alliance to stand aside anywhere and everywhere they asked."
Of the seats Alliance has withdrawn from North Belfast is perhaps expected to be one of the closest fought.
" The Ulster Unionists have made it clear that they wanted Alliance to stand aside anywhere and everywhere they asked "
The party's former candidate there Councillor Tom Campbell said: "I believe my action will strengthen the hand of more moderate pro-Agreement parties in the area."
Sitting Ulster Unionist MP Cecil Walker, a strong supporter of the Agreement, is being challenged by anti-Agreement Democratic Unionist Nigel Dodds.
With a growing nationalist vote in the constituency, there is also expected to be strong support for the SDLP's Alban Maginness and Sinn Fein's Gerry Kelly.
Mr Kelly meanwhile has accused Alliance of attempting to make a virtue out of necessity over their withdrawals.
He said: "I would suggest that the reasons have more to do with their abysmal showing in the elections to the European Parliament last year than out of concern for the Agreement. Alliance are a spent force."