A 24-hour strike by Network Rail workers was to have taken place from 17:00 BST on Thursday, followed by a 48-hour walk-out next week.
Acas said four days of talks helped “formulate” revised proposals for the RMT and other unions to consider.
The RMT has 16,000 members at Network Rail in operations and maintenance.
RMT general secretary Mick Cash said the union would consult on the details of the revised package.
Members of the TSSA and Unite unions will also be consulted.
Network Rail chief executive Mark Carne said: “I am very pleased that the industrial action has been suspended. With Acas’s help, we have had very constructive talks with the unions over the weekend and I hope they will be able to agree this deal.”
Transport Secretary Patrick McLoughlin said: “I am pleased that the union has engaged with Network Rail in order to avoid a dispute.
“I hope that this deal will be now ratified by the union swiftly.”
The revised offer is for a 2% increase in pay, backdated to January this year.
This will be followed by a rise in line with RPI inflation next year, based on the November 2015 figure – currently forecast to be about 1.5%.
There would also be no compulsory redundancies for the duration of the agreement, and the unions agreed to participate in discussions with Network Rail to deliver savings through areas such as sub-contracting.
A “comprehensive job security package” is also to be agreed.
Network Rail originally offered workers a four-year deal of a single non-consolidated £500 payment followed by three years of rises in line with RPI inflation.
This was turned down by both the RMT and TSSA, and the unions called a strike starting on the 25 May bank holiday.
It was suspended after Network Rail tabled proposals for a 1% rise this year, and a rise of about 1.4% next year, but this offer was not accepted by the RMT