Swan has asked the Greens to not block the Mineral Resources Rent Tax in the Senate as they call for changes to mining tax legislation.
It comes after the Australian Financial Review reported last week that the government may cut the multibillion dollar tax cuts for small businesses.
The Greens have stated they are unwilling to pass the MRRT until the government includes promised company tax cuts for small business in the mining tax legislation, the AFR reports.
According to Greens head Bob Brown "the Gillard government has itself to blame if the Senate delays passage of the mining tax package in the coming weeks.
"Where is the government’s promised tax cut for small business (from 30% to 29%) due to start in July? It is reasonable to want to see legislation for the small business tax cut before handling the rest of the package," Senator Bob Brown said in Hobart on Sunday.
Swan retorted that it was important to have support for the mining tax legislation as it suffers Opposition challenges.
"These are important measures. That’s why we need to see priority for passage of this legislation through the Senate and we need to see the support of the minor parties and the Greens."
He went on to say that it was important the legislation passed the Upper House within the next two weeks to come into effect for 1 July, The Age reported.
The Greens have also pushed for more changes to the mining tax, predominately to widen its scope from just iron ore and coal, and to include gold and uranium.
Bob Brown recently came under fire for these statements.
Sandra Close, a director of Surbiton, said she was ‘extremely concerned by the claims of the Greens’ and their calls for gold to come under the auspices of the MRRT.
"I have already highlighted the misleading and incorrect information on the gold industry contained in a report the Greens released late last year," Close said.
"Just last week, Senator Bob Brown specifically called for gold to be included in the MRRT, basing his arguments on the fundamentally flawed report.
"It is a real concern when politicians use faulty figures to justify their policies,” she said. "It’s quite clear that the Greens have little understanding of the gold industry and they don’t even seem to appreciate that gold is at the other end of the scale to the bulk commodities of coal and iron ore."
Close went on to say that the Greens’ estimates of the size of the Australian gold industry and that it is equal to the amount of gold export "is crazy, because Australia imports, refines, and re-exports a large amount of gold which has been mined in other country.
"Either the Greens are just naive or they are deliberately trying to inflate the gold industry numbers, so they can justify their claims for what tax it might yield," she said.
Swan is unlikely to budge on the current form of the mining tax, adding that some amendments from the Senate were expected.
"The fact is we have settled on the design of this tax," he said.