According to ExxonMobil, 40 workers contracted to Deborah Services Limited (DSL) have gone on strike at its ethylene plant at Mossmorran in Fife, along with colleagues at the Shell plant at Mossmorran.
The firm said the action was not impacting upon safety at the facility.
Speaking from the World Economic Forum in Switzerland, Mr Brown told the BBC he understood why people were worried: "They look round and say, well, why can't we do these jobs ourselves."
But he said instead of spontaneous strike action, "what we've got to do over time, as I've always said, is that where there are jobs in this country, we need people with the skills, developed in this country".
The prime minister said the government was meeting this challenge by increasing apprenticeships so that the country's skill set would be "ready for the upturn in a more effective way that we were in the past".
Mr Brown added: "You'll find that no government in history is doing more to try to find ways that we can help people who are unemployed back in to work as quickly as possible."
Bobby Buirds of the Unite union said: "I can't say one way or the other whether there's going to be further action and if the lads believe things are developing to their benefit, there might be a change of heart but I don't see that at the moment."
It's important that we have talks and my plea to everyone is not to escalate it
Jim Murphy Scottish secretary
Scottish Secretary Jim Murphy said: "It's time for cool heads rather than wildcat strikes and walkouts.
"What we have to do is make sure the law is not being broken by the action of this employer, which is why we have called in Acas.
"But what we also have to recognise is that this free movement of labour across Europe is a great thing for Scots and for people throughout Britain."
There have been fears that the unofficial action might spread after the weekend.
Mr Murphy added: "It's important that we have talks and my plea to everyone is not to escalate it."
And he dismissed worries about the action affecting the public through the petrol pumps.
"We're confident that we have the necessary contingency plans in place. We're working very hard to make sure there are no fuel shortages," he said.
A spokesman for Ineos, which runs the Grangemouth plant, said those involved in the walkout were NAECI (National Agreement for Engineering and Construction Industry) workers.
In a statement, he said: "The plants at Grangemouth continue to operate normally and contractor safety cover has been agreed.
"We are disappointed that the NAECI contactor population have chosen to walk out today, especially as Ineos at Grangemouth has always worked with the trade unions to ensure that local and UK labour are utilised on site.
"And, on the few occasions when it has been necessary, we have always agreed up front with the workforce the use of foreign labour as a top-up."
The Grangemouth walkout included about 100 workers with contractors employed by BP.
They work at the Kinneil terminal - part of the Grangemouth complex where North Sea oil from the Forties pipeline system comes ashore.
A BP spokesman said: "The workers are not involved in day-to-day operations and the Forties pipeline system will continue to operate as normal."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.