After last week's disruptions, a rail worker's union said it was "not in any hurry" to call for more strikes in July.
Senior assistant general secretary at RMT Eddie Dempsey said that the union didn't "take these steps lightly".
Dempsey is also in charge of talks with Network Rail and said that it has been a very intense week of discussion.
Both sides are working together to find an agreement to stop further strikes.
As part of a dispute about job cuts, pay, and conditions, thousands of RMT members who work for Network Rail, 13 train companies, and other rail companies, walked out last week on Tuesday, Thursday, and Saturday.
The strike closed half of the rail network, and the knock-on effect meant that services were disrupted the next day.
The union warned that more strikes could be coming.
When asked by BBC Today whether further strikes could occur in July, Mr Dempsey replied: "We've already told people that we're in no hurry.
"I believe we have made an important point with the strike action that we took. These steps are not taken lightly. We don't rush to get into the boardroom or take any further actions.
Network Rail and the RMT are trying to come to an agreement about job security first, before they discuss pay and conditions.
Dempsey stated that the discussions this week were "fairly intense".
"We are making progress in terms of our discussions. "There are still fundamental problems between us, and that's the reason we're looking for feedback. But we haven't yet gotten to the question of pay," Mr Dempsey stated.
"This is going to be an important issue. We will have to wait to see if there is a solution.
The strike came after Tim Shoveller (Network Rail's lead negotiator) said that he was "cautiously optimistic” about reaching an agreement with the RMT union in order to avoid further strikes.
According to Mr Shoveller, talks since last week’s walkouts have been constructive.
Network Rail sent the RMT a note on 20 June inviting them to attend a formal consultation meeting about reforms to working practices that could lead to job losses.
According to a spokesperson, the BBC heard this week from a representative that, although the letter was not withdrawn, both sides had agreed to temporarily put it aside in order to allow talks to continue. It would only be used if negotiations stall.
BBC was informed by Mr Shoveller that the original meeting to officially start the process had been cancelled.
He stated that there was no need for it as negotiation was the best way to reach a consensus. "The letter is still in effect, but that does not prevent us from having the discussions we need," he said.
After "pragmatic discussions" with the RMT, Mr Shoveller said that this was a "pragmatic situation" and that there was no need for a formal consultation at the moment.
