The Welsh Government has urged health unions to accept the new pay deal for staff, calling it “the only deal in town”.
Unions representing NHS workers in Wales have largely suspended industrial action while they consult members on the new offer, which was made on Friday.
Unite was the only NHS union staging walkouts in Wales on Monday.
“The end of the financial year is coming very soon, and obviously the money disappears at the end of the financial year so there is an issue for people to consider there.
“So I do hope that people recognise that we’ve worked really hard on this, that we are restricted in how much we can offer because of the money we get from the UK Government.
“And I do think that there’s a lesson here for the UK Government – UK Government needs to understand that, in order to get any kind of deal, you need to sit down, you need to talk and you need to listen.
“They’re not doing any of that, and I would encourage them to do that.”
Negotiations resulted in a new pay offer from the Welsh Government for 2022/23 of an additional 3% increase, unions said.
The GMB was due to hold a strike on Monday, while members of the Royal College of Nursing (RCN) were set to walk out on Monday and Tuesday.
The two unions announced on Friday that their action in Wales would be suspended, although their members in England would go ahead with strikes on the same days.
A strike by physiotherapists in Wales on Tuesday has also been called off.
Meanwhile, the Royal College of Midwives (RCM) said a strike by its members across Wales will not go ahead and it is suspending action short of a strike planned for February 7-14 while it consults members on the new offer.
But Unite said it would be “disingenuous” to suspend strike action, saying a deal is “tantalisingly close”.
The union’s general secretary, Sharon Graham, told the PA news agency: “The reason that we’re still out in Wales is that it would be disingenuous for us to put an offer to pause the strike in the full knowledge the offer was going to get rejected.
“What we want is not a sticking plaster – we want to have a deal on the table that will be accepted.
“I spoke to the health minister in Wales on a number of occasions yesterday; we’re tantalisingly close.
“The sticking point really is (of the) the extra 3% – half of it is on non-consolidated, so therefore it’s a one-off payment.
“And what we’re simply asking is to put more of that on the wages, so that people have that forever, it’s in their pay packet, because that will address some of the concerns.”
Asked about Unite, Baroness Morgan said: “Unite now, having failed to call off their strike action, obviously are no longer part of the negotiation.
“So the negotiations continue with the other unions, but they are now not formally a part of that negotiation.
“Obviously, we would like and we’re always ready to continue talking with them. But I’ve been absolutely clear with Unite that there is no more money.”
Jason Killens, chief executive of the Welsh Ambulance Service, said: “While we recognise that RCN and GMB colleagues have taken the decision to postpone strike action in light of a revised offer from Welsh Government, at this stage we are still facing a two-day strike by Unite members, which will inevitably result in significant pressure on our services today and tomorrow.
“We understand the reasons for strike action and thank the Welsh Government for their commitment to finding a resolution which has got us this far.
“That said, with two days of action still planned by Unite, we would ask the public to think very carefully before calling 999.
“Our services will be significantly affected and, while Unite has agreed some exemptions, we will have very limited ability to respond to any call that is not immediately life-threatening.
“This means that you may need to take a loved one to hospital if it’s safe to do so. People can help us by only calling 999 in a life or limb-threatening emergency or where there really is no other option.
“Please use NHS 111 Wales as your first port of call, or consider visiting your nearest minor injuries unit, where there is no need for an appointment, your local pharmacy or your GP.”