Separately, the conditions of two soldiers who were seriously wounded during combat in Afghanistan on Monday remain stable. According to the Armed Forces, the soldiers were hit by shrapnel from so-called RPGs, or rocket-propelled grenades.
"The situation is trying for our unit, but they are also doing a great job," Supreme Commander Sverker Göranson said when he arrived at the meeting with the Riksdag's defence and foreign affairs committees to provide information on his views on the situation in Afghanistan.
"Both the civilian and military factions are convinced that what we are doing, we are doing properly and we are coming across more and more people who have confidence in us," he added.
The news of the two soldiers injured on Monday comes as a new Aftonbladet poll conducted by Sifo reveals that nearly half of the Swedish population believes that the government should bring the country's troops in Afghanistan home.
One of the injured soldiers, a 26-year-old man from the Gothenburg area, has very serious injuries, but they are thought to be life-threatening, according to Armed Forces spokesperson Mattias Robertson.
The other injured soldier, a 29-year-old man from Medelpad in central Sweden, also has serious injuries.
"The soldiers' work will continue as usual and they will carry on with their activities and operations," said Robertson.
A brief ceremony for slain Swedish soldier Kenneth Wallin was conducted at the Swedish base in Afghanistan's Mazar-i-Sharif on Tuesday morning before his coffin was transferred to the airport outside Camp Marmal for further transport to Sweden.
Wallin was killed on Saturday.
Defence committee chairman Håkan Juholt, a Social Democrat, stressed the importance of a broad political agreement on the Swedish military effort in Afghanistan.
"My conviction is that because it is so serious, we need broad political support," he said.
Juholt hopes that the government will present a bill that is designed so that all political parties will support it.
"It is deserving of Sweden's reputation in the world, the soldiers who are there, their relatives, and the Swedish people," he said.
However, Juholt refused to comment on a timetable for a troop withdrawal.
At a press briefing in the morning, Left Party leader Lars Ohly said that he would be willing to drop demands for the withdrawal of Swedish troops starting in 2011 and ending in 2013.
He said that if the government is prepared to discuss a cut-off date, he is willing to listen.
Separately, 47 percent answered yes to Aftonbladet's poll conducted by Sifo asking 1,000 people over 15 whether Sweden should bring its troops in Afghanistan home.
Thirty-six percent said they should remain.
More women than men and more younger than older people believe that the troops should return home, according to the survey.
In July, 42 percent responded that they felt that Sweden should keep its combat forces in Afghanistan.