Mr MacAskill later accused the two parties of "playing politics" and said their behaviour was "appalling".
However, Labour and the Tories warned Mr MacAskill that, in this era of minority government, ministers had to listen to the views of parties outside the government.
At Holyrood's justice committee yesterday, Mr MacAskill argued for a rise in the length of time prisoners could spend on the home detention curfew scheme – electronic tagging – from four and a half months to six months.
He told MSPs there was a growing problem with prison overcrowding and an extension to the tagging rules would ease that burden.
Labour and the Conservatives offered to agree to the extension, but only if a so-called "sunset clause" was inserted. This would have seen the order end when a new prison at Addiewell was completed, allowing parliament to revisit the issue.
Mr MacAskill refused, so the four Labour and Tory MSPs on the committee voted against the order. The vote was tied, with Tories and Labour opposed and the four SNP and Liberal Democrat MSPs in favour. Bill Aitken, a Tory MSP and committee convener, had the casting vote and opposed the order.
Mr MacAskill will bring the order back to the full chamber next week and hopes to get it past the full parliament with the help of the Lib Dems and the Greens.
Figures released yesterday show there are about 330 prisoners on home detention curfew.
Yesterday's plans would have seen that rise by between 50 and 120.