In a statement read by the telecommunications minister, Bouteflika warned that peaceful protests risked being infiltrated by people bent on sowing chaos in a country that "paid a heavy and unhappy price to preserve its unity and re-establish peace and stability."
The Algerian leader has been in power since 1999 and is largely credited with maintaining the peace since a civil war that left an estimated 200,000 dead. But he has been all but absent from the public eye since a stroke in 2013. He has been hospitalized in Switzerland since last month for what the government described Feb. 21 as medical tests.
His campaign director offered an upbeat assessment, saying there was "nothing to worry about."
The messages from Bouteflika and his campaign chief came hours after lawyers staged a protest march to the Constitutional Council, calling out "No to fraud!" as they headed to the offices where presidential hopefuls formally file as candidates. Police allowed the marchers past the barricades.
New protests were planned for Friday after prayers.
In the statement, Bouteflika called for vigilance against internal and external "infiltrators" who could "provoke chaos."
Bouteflika did not appear in person on Sunday to file for his candidacy, as the lawyers and others say is required under Algerian law.
In response to the first wave of public demonstrations, Bouteflika released a statement that day promising that if he is re-elected April 18, he would organize a public referendum on a new constitution. He promised to hold new elections after a national conference on reforms, and would not stand as a candidate in that vote.
But the demonstrations have continued unabated, and protesters are calling for a general strike and acts of civil disobedience if they don't get their way.
That has included a seemingly spontaneous campaign of Algerians contacting Geneva's biggest hospital, which had to shut its Facebook page and triple its switchboard staff after getting flooded with calls and comments about Bouteflika's health.
On Tuesday, Geneva University Hospitals received some 1,500 calls about Bouteflika, about a 50 percent increase in its usual daily call volume, said the hospital spokesman, Nicolas de Saussure. Overflow calls were diverted to a recorded voice message saying the hospital does not provide information about its patients.
De Saussure said most calls sought information, though an "extreme few" were aggressive. The hospital has not confirmed Bouteflika's presence.
Back in Algeria, at least two parliamentarians and a prominent veteran of the country's civil war have thrown their support behind the crowds. But Bouteflika retains significant support in the military, which is widely seen as a top powerbroker. Algeria's army chief of staff, Gen. Ahmed Gaid Salah, this week evoked the years of bloodshed before Bouteflika took office.
When neighboring Tunisia and Libya overthrew autocratic leaders in 2011, the Algerian government boosted public spending and avoided Arab Spring uprisings.
Jamey Keaten in Geneva contributed.