Members of the Rail, Maritime and Transport union (RMT) on Arriva Rail North (Northern) have staged a series of walkouts in a dispute over guards on trains, with more stoppages due on every Saturday for the rest of the year.
The union offered to suspend industrial action on Northern Rail this weekend subject to the company agreeing to a "series of crucial guarantees" on the second person on their trains.
RMT's executive said in a statement: "This union has always been available for talks and we are prepared to engage in talks immediately via Acas.
"We are available across the weekend and would welcome talks commencing as soon as possible and further reiterate our numerous previous requests for tripartite talks with both the company and the Department for Transport.
"In addition, we will be prepared to suspend the industrial action planned for December 1 providing that clarity is received from the company regarding a new proposal that will see the retention of a second person on-board trains."
The union said it wanted a 100% guarantee that no trains will run without the second member of staff on board, that the second member of staff will be clearly designated as safety critical to the running of all services and will retain a direct role at the platform and train despatch.
The union said it wanted a response by 12pm on Friday to be able to suspend industrial action.
RMT general secretary Mick Cash said: "I want to pay tribute to the RMT members and our supporters from the travelling public whose solidarity and determination have been instrumental in getting the focus of the dispute back on to the guarantee of a second person on the train.
"It is now imperative that the company clarify the role and safety critical status of that second person as set out by our executive to allow for a suspension of this weekend's action and for talks to take place."
A Department for Transport spokesman said: "We are working with Transport for the North to call on the RMT to ends its needless industrial action on Northern.
"The Rail Minister wrote to the Rail North Partnership (through which Transport for the North and the Department co-manage the Northern franchise), to reiterate the Government's commitment to having a second person on board Northern trains, whose role is focused on looking after passenger needs. He also committed Government to playing its part in funding this.
"We are pleased that Transport for the North has also written to the Rail North Partnership on this matter, and believe these commitments should ensure that these cynical strikes come to an end."