"We want to be able to strengthen the law so that it is substantially harder," Karin Enström, the Moderate chair of the Riksdag's foreign affairs committee, told the TT news agency.
She expects her committee to reach a broad consensus by Thursday to urge the government to strengthen current legislation.
Among the four governing parties, the Liberal Party (Folkpartiet) and Christian Democrats have been pushing for stronger weapons export controls.
The Liberal Party's Fredrik Malm is satisfied with the current set of negotiations on the matter.
"It's clearly going in a direction that we in the Liberal Party are happy with. We're in agreement that we want to see tougher legislation when it comes to weapons export controls," he said.
He also felt that selling arms to Pakistan and the United Arab Emirates wasn't "appropriate".
Last year, Swedish companies sold at least 2.3 billion kronor ($370 million) worth of arms to those countries, representing more than 15 percent of Sweden's total arms exports.
The Christian Democrats, meanwhile, have been pressured by various interest groups, with Swedish foreign aid organisation Diakonia at the fore, to push for tougher weapons export rules.
In a letter sent to political parties earlier this spring, Diakonia, the Christian Council of Sweden (Sveriges Kristna Råd), Amnesty, and the Swedish Peace and Arbitration Society (Svenska Freds- och Skiljedomsföreningen), have all challenged politicians to make their stance on the issue clear.
"It's a good draft that the Alliance and the Social Democrats have agreed on," Christian Democrat Desirée Pethrus, of the Riksdag's foreign affairs committee, told TT.
She confessed, however, that it's not that simple to decide which countries are democracies and which aren't, and that it's even harder to define human rights.
Pethrus regretted that the Green Party and the Left Party don't appear ready to support the agreement.
"They're missing a historic opportunity," she said.
Hans Linde of the Left Party said that his party will register their dissent to the minutes when the committee has completed its proposal on Thursday.
The Left Party would rather implement "stronger democratic criteria" which puts language in export regulations that rules out arms exports to dictators.
He believes the government and the Social Democrats current formulation is too vague.
"We don't know when there will be tougher laws or how they will be strengthened, but we can probably be pretty sure that even with the legislation, Sweden is still going to export to dictators in the future," he said.
The foreign affairs committee vice chair, Social Democrat Urban Ahlin, is happy with the agreement, set to be formally completed on Thursday.
He pointed out that his party has tried in vain for many years to strengthen Swedish arms export laws and that the Liberal Party's comments in March represented an important shift.
"And we're very happy about it," said Ahlin.