Egyptian activists have called for an international day of action to defend their country's revolution, as global opposition mounts towards the military junta.

In a statement appealing for solidarity from the worldwide Occupy movement that has taken control of public squares in London, New York and hundreds of other cities, campaigners in Egypt claim their revolution is "under attack" from army generals and insist they too are fighting against a "1%" elite intent on stifling democracy and promoting social injustice.

The announcement came as Alaa Abd El Fattah, the jailed Egyptian revolutionary who has become a rallying figure for those opposed to the junta, had his appeal against detention refused by a military court. He and 30 other defendants accused of inciting violence against the military will remain in prison for at least 10 more days. The authorities could then choose to extend their incarceration indefinitely. This week a secret letter written by Abd El Fattah from inside his cell at Bab el-Khalq jail was published by the Guardian and the Egyptian newspaper al-Shorouk, laying bare the growing chasm between the ruling generals and grassroots activists who believe that their revolution has been hijacked.

In Thursday's communique, which was jointly signed by a number of activist groups and published on the website of the "No to military trials" campaign, Egyptian protesters say that while global media attention has shifted elsewhere since the toppling of Hosni Mubarak in February, their struggle has continued.

"Again and again the army and the police have attacked us, beaten us, arrested us, killed us," reads the statement. "And we have resisted, we have continued; some of these days we lost, others we won, but never without cost. Over a thousand gave their lives to remove Mubarak. Many more have joined them in death since. We go on so that their deaths will not be in vain."

The statement reaffirms activists' decision to withdraw all co-operation from the military justice system: "We now refuse to co-operate with military trials and prosecutions. We will not hand ourselves in, we will not submit ourselves to questioning. If they want us, they can take us from our homes and workplaces."

It ends with a call for an international day of action on 12 November. "Nine months into our new military repression, we are still fighting for our revolution," the activists conclude. "Our strength is in our shared struggle. If they stifle our resistance, the 1% will win – in Cairo, New York, London, Rome – everywhere. But while the revolution lives, our imaginations knows no bounds. We can still create a world worth living."

Sandy Nurse, of Occupy Wall Street, said: "The Egyptian people have changed the face of the regime and the revolution is momentous but unfortunately it is far from over. Changing the face of the regime, getting rid of Mubarak, is like changing the curtains: the military is in control of the country and has been for a long time."

Nurse, who is on the direct action committee of OWS, expressed her personal solidarity with the people of Egypt and added: "I believe Occupy Wall Street would be in solidarity with the continued struggle of the Egyptian protesters."

Anup Desai, a press spokesman for OWS, said: "The effort put out by the entire country in Egypt gave us motivation. Egypt has won the first step. I was not aware what was happening so I am grateful for this opportunity to learn and I thank the Egyptian activists. What is happening with the military and the military courts is 100% wrong and we need to share this and tell people about it."

Desai, who is also a professor of philosophy at City University of New York, expressed solidarity with the activists and said: "We need to keep coming together."

Naomi Colvin, from the Occupy London movement, said: "All decisions are made through a general assembly but I'm sure we will strongly support the call from our friends in the Middle East to stand in solidarity with them through an international day of action.

"Egyptians provided us with an example of courage that has inspired not only our own protest but many others around the world, and we owe it to them to support their ongoing struggle in any way we can."

Links between political upheavals in the Arab world and the campaign against financial injustice in the west have strengthened in recent weeks, with demonstrators on both sides claiming inspiration from the others' struggle. On Wednesday protesters in Oakland waved an Egyptian flag during their general strike, prompting some Cairo-based bloggers to reflect on the similarities between the police tactics used in the US and Egypt. On Thursday activists camping outside St Paul's Cathedral in London conducted a live video link with anti-regime protesters in Syria, while plans are under way for a solidarity rally on Saturday in support of Egyptians being held by the junta.

Meanwhile, in Egypt, more political leaders have spoken out against draft constitutional principles released by the interim cabinet that would see the military's influence over civilian government permanently enshrined in law.

Presidential candidate and former UN nuclear energy chief Mohamed ElBaradei called the document – which would shield the army from parliamentary oversight, give generals a final say over major policies and allow the military to dominate the writing of a new constitution – "distorted" and demanded its withdrawal. "There is a difference between a civilian democratic state that guarantees man's basic rights and military guardianship," warned the Nobel laureate.

Secular political forces had initially called for a set of "supra-constitutional" principles to be written in an effort to dilute the influence of Islamist parties, who are expected to do well in the upcoming parliamentary elections and hence play a major role in the creation of a new constitution next year. But they have since become alarmed at the military's apparent attempts to cement its long-term position of power in the country, and many are now demanding the resignation of deputy prime minister Ali el-Selmi, who was responsible for releasing the contentious document.

The Muslim Brotherhood has also come out against the draft constitutional principles, saying they amount to a "rape of the people's will".