Under the plans, passengers from west Wales could travel straight to Bristol Temple Meads without changing at Cardiff, as they currently need to do.
In a consultation document, TfW said its aim was to “connect communities” beyond the capital to provide new opportunities for work and leisure. It hopes to introduce the services by December 2026.
GWR, which is due to be brought under public ownership later this year, currently runs two services per hour between Cardiff and Bristol, and occasionally three.
GWR said it had concerns that the plans could affect train services in the Bristol area and were “likely to have a significant effect on GWR’s revenue income”.
It also said the new services would mean less money for the UK government.
“It should be noted that due to its devolved status, under existing revenue allocation mechanisms the majority of the revenue growth for the industry will not return revenues directly to HM Treasury,” the rail operator said.
The Rail and Road Office will make a final decision on TfW’s application.
On the train from Carmarthen to Llanelli, people gave their reaction to the idea.
Miriam Kinn, who recently moved to Solva in Pembrokeshire from Bristol, said the new services “would be ideal because we [have] lots of friends [there]”.
Cath Little, from Cardiff, said it would benefit people going on the ferry to Ireland from Fishguard.
“It would save changing in Cardiff so I think it’s a great idea,” she said.
Karen Jones, who lives in Carmarthen, agreed but said there were often problems with delays or cancelled trains.
Mark Hooper, the Welsh government’s Deputy Minister for Transport, said it was “extremely disappointing” that GWR would seek to “disrupt these plans to improve things for passengers on both sides of the Severn”.
He added: “If Great Western Railway’s objection succeeds, it would negatively impact tens of thousands who could benefit from this service.
“I will be writing to the UK Transport Minister to urgently ask for clarification and call for some common sense on this issue.”
A GWR spokesperson said: “We welcome any enhancements to provide additional levels of service for customers along a key route, but this needs to be done so as not to be detrimental to existing services or already agreed future services which will serve south Wales.”
