Borg was presenting the government's assessment of the country's economic health in a meeting in Harpsund ahead of next month's election. He predicted that the number of migrants arriving into Sweden will increase over the coming months.
"We can't rule out that there will be 2,500 - 3,000 people a week at the start of September," he said in a press statement.
Borg added; "That involves costs but there is no reason not to stand up for the common consensus that we have in the asylum policy and that in time it will give a considerable gain for Sweden."
The ministry of finance has anticipated that the costs of integrating refugees into Sweden will likely run into billions of kronor. An annual bill is expected to reach 12 billion kronor ($1.7 bn) a year by 2017 with Borg stating that restricting the number of refugees is not on the agenda.
"We don't leave people in need, we don't close doors," said Borg.
Last week the Swedish Migration Board asked for an extra 48 billion kronor above the 91 billion allowance the board has already been granted for the next four years to help cover the costs of the refugee influx.
Shadow finance minister Magdalena Andersson criticized Borg's handling of the economy since he took office, and said the Alliance's initiative on tackling refugee costs was "election tactics."
"They don't want to talk about unemployment, schools or tax cuts...what's happening now is that the new moderate project is falling apart before Borg, Reinfeldt and Bildt," Andersson told the TT news agency, and added that unemployment was higher now than when Borg took office eight years ago.
In his press statement Borg hinted at tax increases on banks, alcohol and tobacco but pledged not to touch taxes on jobs, businesses and fuel. He also suggested a higher road tax on vehicles which are not considered to be environmentally friendly.
Borg added that he expected the Swedish economy to grow by 1.9 percent this year and that the unemployment rate will be 7.9 percent in 2014, decreasing to 5.8 percent by 2018.
The finance minister, who has been in office since 2006, said that the tax hikes were needed to boost the slow recovery of the economy. He predicted that GDP growth would be lower than expected next year but that 150,000 new jobs would be created by 2016.
The government is expected to present its full list of economic proposals on Monday. Swedes go to the polls on September 14th.