Of particular concern, they say, are measures which would mean a significant reduction in the pension for many Australians from migrant backgrounds.
Questions have been raised about whether some could receive any payments while overseas.
The Government says the move is part of a budget-savings measure.
The proposal, now before federal parliament, would limit the amount pensioners could spend overseas before their pensions were affected.
Under the plan, the time limit they spend in another country and their eligibility to receive their full pensions would be reduced from the current 26-week threshold to six weeks.
After that time, the payments would reduce progressively.
If passed, the law would come into effect in January 2016.
The change would not affect people who have lived in Australia for 35 years or more.
Michael O'Neill, the chief executive of an advocacy group for older Australians, Nationals Australia, says it is unfair.
"It would, in my view, be very difficult, for example, to see how you differentiate between someone who's lived and worked in this country for 25 years, or 30 years. That's a very significant contribution. And to just rule the line at 35 years seems to be very unfair to people in those circumstances of quite long contributions."
Greens treasury spokesman Adam Bandt agrees.
"We've got a large number of people in my electrorate who came to Australia many, many years ago from Greek communities, Italian communities, Vietnamese communities, who are now reaching the ends of their -- or reached the end of their -- work life and presumed that, if they did the right thing here, that they would be able to get the pension and then enjoy it as they saw fit, and they're going to be hit hard. And given that around 40 per cent of aged pensioners weren't born in Australia, this is a measure that's going to impact on a lot of people."
Michael O'Neill says pensioners have every right to spend their time wherever they want without being penalised.
"If they wish to go and spend time with their family members elsewhere in other parts of the world, then that's not an unreasonable thing, given that now more than 25 per cent of Australians are from a non-English speaking background."
Australia has international social-security agreements with *30 countries.
That allows people who migrate between those countries to access their benefits while overseas.
The aged pension cannot be claimed in countries that do not have an arrangement.
Mr O'Neill says those people not covered will be further disadvantaged.
Mr Bandt says it will be an election issue for the Greens.
"We're talking about people who may well have worked their whole life in Australia and are wanting to go overseas for a variety of reasons, and the basic principle of our system should be that, if you've done enough work here in this country to justify earning the pension, then you should have the freedom to enjoy your retirement in the way that you want, and we're very concerned about moves to restrict people spending more than a few weeks overseas because we don't think it really comprehends the various reasons that people would want to move overseas."
Labor's pensions and families spokeswoman, Jenny Macklin, says the Opposition, too, opposes the proposals.
"We understand that, for many pensioners, they've saved up for years and years to go on one big trip in their retirement. Other people who've contacted us are wanting to visit family and friends. Some migrant pensioners, of course, need to go and see their families as they are getting much older, and we know that people have worked very, very hard all of their lives and deserve respect at this time of their retirement."
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