Russia's embassy in Berlin said in a statement: "We call on our partners to avoid any politicization of this incident and to rely solely on credible facts, which we hope will be delivered as soon as possible."
The Charite hospital that has been treating Navalny reported improvements in his condition.
But the charismatic Yale-educated lawyer, who has been Russia's leading opposition politician for around a decade, is still in the intensive care unit and remains on a ventilator.
Read also: Alexei Navalny Given Protection in German Hospital after Likely Poisoning
Doctors say that over time the body can clear out the nerve agent, which disrupts communication between the brain, the main organs and muscles.
"Recovery is likely to be lengthy. It is still too early to gauge the long-term effects which may arise in relation to this severe poisoning," added the hospital.
Skripal, Litvinenko poisoning
Relations between the European Union and Russia are particularly sour at present, the two sides at odds over a host of issues from Russia's annexation of Crimea, its backing of Syrian leader Bashar al-Assad, as well as alleged election meddling.
The EU has had sanctions targeting whole sectors of the Russian economy in place since 2014.
Two years ago, the Kremlin was also accused of being behind the attempted murder of ex-double agent Skripal and his daughter Yulia in Salisbury, southwest England, using a Novichok nerve agent.