Löfven met representatives of the royal family – King Salman bin Abdul Aziz, Crown Prince Muhammad bin Nayif and Vice Crown Prince Muhammad bin Salman – on Sunday.
“We have brought up issues such as women's rights, the death penalty, even corporal punishment. We're doing it in the way that we believe will have the greatest effect,” Löfven told Swedish media after the meeting.
The absolute monarchy Saudi Arabia recalled its ambassador to Stockholm in March 2015 after what it called "flagrant interference in internal affairs" by Swedish Foreign Minister Margot Wallström.
The foreign minister had criticized the kingdom's treatment of blogger Raef Badawi, who was sentenced to 1,000 lashes and ten years in prison for insulting Islam. "One must protest against what are nearly medieval methods" of punishment, Wallström said.
She also called Saudi Arabia a dictatorship and blasted the abysmal state of women's rights in the country, which then blocked Wallström from addressing the Arab League and fumed over the public debate in Sweden about scrapping a military cooperation agreement.
When Sweden officially cancelled the military cooperation agreement in 2015, Saudi Arabia retaliated by temporarily refusing to issue visas to Swedish businesspeople.
"It's important that you stand up for what you believe in, even when it costs you," Wallström later told The Local.
Löfven and King Salman on Sunday. Photo: Henrik Montgomery/TT
Sweden is keen to smooth relations for a couple of main reasons: Saudi Arabia is a key export market for them, and the Middle Eastern country is also a major geopolitical player in the region.
With Sweden set to take its place as a temporary member of the UN Security Council next year, the government wants good diplomatic relations with Saudi Arabia ahead of likely talks on Syria, Yemen and Iraq.
Social Democrat leader Löfven, who heads Sweden's self-described feminist coalition government, also visited Glowork on Sunday, a Saudi Arabia-based social enterprise which links female job seekers with employers. However, he was cautious in criticizing Riyadh on women's rights.
“It's important to note that we are two separate communities. Here there's a development that is being carried out in their way,” he said.
Swedish business leader Marcus Wallenberg, who joined Löfven on the trip, visiting Glowork. Photo: Henrik Montgomery