The editors from NTV television, Ekho Moskvy radio station, Itogi magazine and the Sevodnya newspapers - big hitters in the Russian media world - allege that Kremlin officials have instigated "systematic persecution and blackmail" by the tax authorities.
They depict this tactic as a challenge to media freedom, which is often - legitimately - hailed as one of the broad achievements of Mr Yeltsin's rule, although the Kremlin manipulated the press during the 1996 election.
"For the first time in the history of the new Russia, we are witnessing crude and open pressure on one of the main triumphs of Russian democracy: freedom of speech," said the letter, released by Ekho Moskvy. It claimed that the President's aides, including his chief of staff, Alexander Voloshin, ordered the tax police to open criminal cases against them "on any pretext".
Underlying the conflict - which coincides with a flurry of corruption allegations aimed at the Kremlin inner circle - is a pre-election power struggle between two media barons, Boris Berezovsky and Vladimir Gusinsky. In 1996, they teamed up to help ensure the return to office of a deeply unpopular Mr Yeltsin and to keep out the lacklustre Communist challenger, Gennady Zyuganov. Now the former allies are at each other's throats.
All four news organisations which complain of Kremlin bullying belong to Mr Gusinsky's Media-Most publishing empire. Over the last week, both sides have been trading blows with sufficient ferocity to attract a public rebuke from the Russian Prime Minister, Sergei Stepashin.
One important beneficiary of the mud-slinging is beginning to emerge in the burly form of the mayor of Moscow, Yuri Luzhkov, one of the top contenders for the presidency who is also at odds with Mr Yeltsin - a former ally - and his team. The powerful and canny mayor has already taken the precaution of acquiring extensive media properties. Now Mr Gusinsky's media empire, happy to goad the Kremlin, seems to be giving the mayor its support. A formidable alliance could be in the making.
As the manoeuvring gathers pace, suspicions abound among Russian journalists that when the election race heats up, press freedom will suffer as the political elite, with the Kremlin to the fore, strive to use the media for their own ends. Although this is no different from many other countries during election season, the Russians point ominously to a new ministry set up last month by Mr Yeltsin to oversee the media.
The new minister, Mikhail Lesin, has made an unpromising start. He energetically denied any intention to act as a censor. But this did not square with comments he made to Kommersant newspaper (perhaps the most respected in Russia, it has itself just been covertly swept into Mr Berezovsky's empire),which included his announcement that "protecting the state from a free mass media is a very pressing issue".