Human rights activists today accused Chechnya's president, Ramzan Kadyrov, of personally threatening Natalia Estemirova, the Russian human rights campaigner who was abducted and shot dead in Chechnya yesterday.

Oleg Orlov, the director of the human rights organisation Memorial, claimed Kadyrov made the threat during a meeting just months before her death. He said the president's aides had explicitly warned her to stop her work in Chechnya.

"I know who is guilty of Natalia's murder. His name is Ramzan Kadyrov," Orlov said in a statement posted today on Memorial's website. "Ramzan already threatened Natalia, insulted her, considered her a personal enemy. He has made it impossible for rights activists to work in Chechnya," he said.

Estemirova was seized by four unknown men yesterday morning as she left for work. Neighbours at her house in the capital, Grozny, heard her shout: "I'm being kidnapped."

This morning Kadyrov promised to investigate Estemirova's death, which he blamed on forces trying to "discredit" Chechnya and Ingushetia. He described her murder as a "barbaric crime" and a "carefully planned act". Interfax news agency quoted Kadyrov as saying the perpetrators of her "monstrous" murder "deserve no support and must be punished as the cruellest of criminals".

Estemirova's body was found near Gazi-Yurt village, in neighbouring Ingushetia.

She had been shot twice in the head and chest, police said, adding that her corpse had been dumped on the main road.

Human rights activists expressed outrage at her murder, reminiscent of the killing of Anna Politkovskaya, the journalist, writer and bitter Kremlin critic shot dead outside her Moscow apartment in 2006.

Estemirova, 50, was a close friend of Politkovskaya's. The two had collaborated on numerous investigations into human rights abuses in Chechnya. Both were scathing opponents of Kadyrov, Chechnya's pro-Kremlin president.

"Natasha was at the forefront of some of the most intense human rights investigations in Chechnya," said Allison Gill, director of Human Rights Watch in Russia. "She was targeted because of her work. I have no doubt her killing was to silence her. One of the most amazing things about Natasha is that she never stopped doing what she was doing. She never checked herself. She was highly public in her calls for accountability.

"I think the human rights situation is in crisis in Russia," she added. "We have a deathly silence from the authorities whenever activists, lawyers or journalists are murdered. Not a single person is brought to justice."

Last night the US and EU condemned her "brutal" death. "We call for the authorities to try to establish who is responsible," the Swedish foreign minister, Carl Bildt, whose country holds the EU presidency, said. Mike Hammer, the US's national security council spokesman, added: "Such a heinous crime sends a chilling signal to Russia's civil society and the international community."

Russia's president, Dmitry Medvedev, has condemned the murder. He is likely to face tough questioning over the Kremlin's abysmal human rights record during a bilateral summit later today in Germany, with the chancellor, Angela Merkel.

Estemirova was the Chechnya-based head of Memorial, Russia's oldest human rights group.

Operating out of a small office in Grozny, she doggedly pursued stories of human rights abuses in the face of official intimidation and hostility.

She recently collaborated on two damning reports into punitive house burnings and extra-judicial killings in Chechnya, allegedly carried out by Kadyrov's forces. The reports documented how on 2 July his troops allegedly shot 20-year-old Madina Yunusova and her husband near Grozny. Chechen officials claimed her husband had been involved in a plot to kill Kadyrov. Yunusova died three days later in hospital under mysterious circumstances.

"Natasha was always involved in the most sensitive cases. She knew what she was doing. She knew the risks," Shamil Tangiyev, a former Memorial colleague, said. "She was extremely brave. It was in her nature to be an activist."

Estemirova made no attempt to hide her work. Her office near the newly renamed Putin Avenue was well known.

The timing of her murder follows Barack Obama's first visit to Moscow last week as US president. Obama met with Russian human rights activists and set out the US's commitment to "universal values".

The Kremlin responded with hardline pronouncements and President Medvedev visited the breakaway Georgian republic of South Ossetia on Monday. The trip appeared to be a direct rebuff to Obama, who had said that both Georgia and Ukraine should be free to choose their own leaders.

Estemirova, who leaves a 15-year-old daughter, was probably the best-known human rights activist in Russia's provinces.

Earlier this year she attended the trial in Moscow of four people – two of them Chechens – accused of involvement in Politkovskaya's murder.

Speaking to the Guardian in February, Estemirova called the Politkovskaya trial a "farce".

Kadyrov, a close ally of Russia's prime minister, Vladimir Putin, has denied accusations he was involved in Politkovskaya's killing, saying: "I don't kill women."

The Kremlin has recently given Kadyrov unprecedented powers for counter-terrorist operations in Ingushetia, amid a worsening Islamist insurgency across the entire north Caucasus.

Estemirova was a close colleague of Stanislav Markelov, the human rights lawyer murdered in Moscow in January. A masked assassin shot Markelov in the back of the head, not far from the Kremlin, along with Anastasia Baburova, a journalist with the Novaya Gazeta newspaper.

Last night rights activists urged the west to place human rights at the centre of any dialogue with Russia. Gill said: "We can't talk about trade or energy without mentioning the rule of law."