"We would be very cautious about any request, and there has been no request and no indication that there will be a request coming.
"In Syria, everyone understands it is a very complex situation [and] hard to see a path to success. Our preference, of course, is a political-type settlement where there isn't ongoing killings and atrocities."
Australian Prime Minister Malcolm Turnbull has been more direct, saying over the weekend that Assad's crimes were "so enormous and of course now so recent, it is difficult to see how a political solution can be crafted that has him with a continuing role."
New Zealand had supported the air strikes as a "proportional response to a specific incident - the chemical weapons atrocity", English said.
Yesterday Defence Minister Gerry Brownlee said, in his assessment, the air strikes were probably a one-off, and he was not expecting any US request for New Zealand to contribute anything more than it already is against Isis in Iraq.
"It would be fair to say we are keeping a close watch on it - the whole world is keeping a close watch on it.
"But it looks like it's much more along the lines of a one-off shot-over-the-bows of both the Syrian regime and their supporters to say this sort of behaviour is not acceptable."
New Zealand was notified in advance of the strike as a matter of courtesy because it was part of the US-led Coalition against Isis in Iraq.
New Zealand and Australia are running a training mission in Camp Taji for Iraqi forces fighting Isis in Iraq, with New Zealand contributing 106 Defence Force personnel to the effort.
Australia which, unlike New Zealand, is a formal ally of the United States, has also been involved in air strikes with the US against Isis in both Iraq and Syria and will advise and assist role near the front line.