"It's a significant disappointment to all of us, because Sweden is usually a voice for international justice tha we can count on," Lotte Leicht, spokeswoman for Human Rights Watch in the EU, told the TT news agency on Tuesday.
"It's a sad day for Swedish foreign policy."
The letter, which was drafted by Switzerland, was signed by 57 countries and sent to New York on Monday.
Erik Zsiga, press secretary to Swedish Foreign Minister Carl Bildt, referred to a decision on December 10th, 2012 by Bildt and his EU counter-parts agreeing that war criminals would be prosecuted.
When contacted about the Swiss initiative, however, Bildt decided that pursuing justice within the Syrian system was preferable to involving the ICC in The Hague, said Zsiga.
Yet Bildt's Moderate Party faces dissenting voices within the four-party government coalition that it leads.
Spokespeople from the Christian Democrats, the Centre Party and the Liberals (Folkpartiet) all said they were in favour of signing the letter to the UN, even though experts say China and Russia are likely to veto any action against the Syrian government on security-council level.
"Of course Sweden should be exerting pressure. We usually fly the flag for human rights," Christian Democrat foreign affairs spokeswoman Désirée Pethrus told TT.
Her counterpart in the opposition Green Party, Bodil Ceballos, said she had brought the issue up with Bildt's top aide, Frank Belfrage, who said the timing of such an initiative was "off".
Bildt remained convinced that the letter would be counter-productive.
"It would put Assad in a headlock and make him less flexible, because we'd be telling him 'your only option is to fight to the death'," Bildt told TT.