Labor leader Bill Shorten echoed his colleague's demands, telling the government to explain the "jaw-dropping" reports as a matter of urgency.
"The place for people smugglers is in prison, it's not to be paid with Australian taxpayer money," he told reporters in Melbourne.
"Logically the message that sends to people smugglers is the Australian government will pay you to carry out your crimes."
Indonesia has launched its own investigation over claims that six crew members of a boat carrying 65 asylum seekers were each paid US$5000 after being intercepted by Australian border protection personnel.
Ms Marsudi approached Mr Grigson - who has just returned to Indonesia after his withdrawal over the executions of two Australian citizens - at a conference in Jakarta on Saturday.
"I just asked him what is it about, tell me what is it about," she told reporters.
"I made use of the opportunity to talk to him directly because we are really concerned, if it is confirmed."
Two senior ministers have denied payments were made to people smugglers but Mr Abbott dodged questions using the cover of "operational matters" - which the government does not discuss.
But the prime minister says he will not apologise for stopping the boats.
"What we do is we stop the boats by hook or by crook," Mr Abbott said on Friday.
Professor of international law at the Australian National University Don Rothwell said if proved, the activity could be tantamount to people smuggling under current regional protocols.
The Australian Greens will try on Monday to win Senate support for a motion requesting the government table documents detailing any payments to individuals on board asylum seeker boats.
Liberal frontbencher Mathias Cormann said the prime minister was simply sticking to the long-standing practice of not commenting on operational matters.
"He didn't confirm or deny, he didn't make comment one way or the other," he told Sky News on Saturday. "He certainly didn't indicate that payments have been made."
-AAP
