Polish Foreign Ministry spokesman Marcin Wojciechowski said Tuesday diplomats would give the Russians a note serving as an official apology over the Monday incident, in which masked marchers surrounded the embassy, lit rockets, threw stones and set a guard booth on fire, Polish Radio reported.
The rioters also set fire to an art installation of a rainbow, considered a symbol of tolerance of homosexuality, as the annual Independence Day march spiraled out of control.
City officials said the clashes resulted in 19 injuries -- including a dozen police officers -- 72 arrests and damages worth an estimated at $40,000.
Wojciechowski said Poland wants a "constructive settlement" of the matter, adding the Foreign Ministry "hopes that the incident will be closed in such a way that it does not harm the relations between our two countries."
Polish Prime Minister Donald Tusk said efforts to organize similar marches in future may be curtailed.
"This situation is unacceptable," he said. "This kind of event cannot take place. Those who tolerate and accept such events will bear responsibility."
Polish Foreign Affairs Minister Radoslaw Sikorski expressed remorse on his Twitter account. "A gang of nationalists who violate the integrity of embassies makes us feel ashamed before the world," he said. "This is a crime and a shame, not patriotism."
Russian Ambassador Alexander Alexeyev met Tuesday with Eva Figiel, Warsaw's chief eastern department diplomat, handing her a note asking for clarification of the situation.
Alexeyev accused Warsaw city officials of not providing adequate protection for the embassy, claiming that even though police knew the parade route in advance, no protective barriers were place around embassy grounds, the Polish broadcaster reported.
Polish ambassador to Russia Wojciech Zajaczkowski was "called on the carpet" in Moscow, where the Russians lodged a "firm protest" and demanded an apology saying the incident violated international protocols guaranteeing the safety of all diplomatic missions in the country.
The Russian Foreign Ministry also demanded punishment for those responsible and compensation for damages to the embassy.
Two suspects appeared in Warsaw District Court Tuesday charged with violating police orders to keep the march peaceful -- one was fined $500 and the other sentenced to six months' detention, the Russian news agency RIA Novosti reported.
Alexeyev told the Rossiyskaya Gazeta newspaper the anti-Russian outburst in Poland was likely fueled by political forces, not just right-wing hooligans.
"I cannot say that it's just the work of some bullies," he said. "Firstly, the route of the march was routed so that the embassy was surrounded by marchers on three sides. This in itself is unusual.
"Prior to that, we all witnessed the appearance of anti-Russian sentiment, especially in the media. Honestly, what happened was not was a surprise to us -- we were preparing for the fact that it all would result in something like this."
Russian RIA Novosti commentator Vadim Dubnov said incident "was not nationalism, like Biryulevo," a Moscow district that erupted in anti-immigrant riots last month.
"This is not even revanchism. This is common neo- Nazism," he said.