The Chilean miners trapped more than 670 metres (2,200ft) underground have started receiving food, water and oxygen from rescuers who are working to reinforce the 8cm borehole that will be their lifeline for the next few months.

The men have not yet been told how long it will take to free them, said Andres Souggaret, who is leading the rescue operation.

Through a newly installed communications system, each of the men at the San José mine reported feeling hungry but well, except for one who had a stomach problem.

The first man answered the call "Shift foreman here," as if he were on from an ordinary day at work. The miners have survived for 19 days on cans of tuna, milk and biscuits stored in the shelter.

Sergio Aguila, a doctor on the rescue team, said the miners had carefully rationed their supplies. "They had two little spoonfuls of tuna, a sip of milk and a biscuit every 48 hours," he said. He did not say how long the supplies lasted.

Asked what they needed, the men listed canned peaches, toothbrushes and a chela – a cold beer.

Chile's president, Sebastián Piñera, said the nation was "crying with excitement and joy" after engineers broke through to the refuge on Sunday. The miners broke out in applause on hearing that their colleagues at the mouth of the mine had also survived the 5 August cave-in.

When told the entire nation was praying for their survival, the men began an apparently spontaneous rendition of the Chilean national anthem, an eerie and moving sound as it filtered up through nearly 700 metres of makeshift communications line, bringing tears to the eyes of rescuers at the surface.

Amid the national euphoria, doctors and experts were trying to safeguard the miners' psychological wellbeing by keeping them informed and busy.

"They need to understand what we know up here at the surface, that it will take many weeks for them to reach the light," said the health minister, Jaime Manalich.

The miners reported that a shift foreman named Luis Urzúa had assumed leadership of the trapped men.

Engineers worked to reinforce the borehole that broke through to the refuge, using a long hose to coat its walls with a metallic gel to decrease the risk of rock falling and blocking the passage.

The lubricant makes it easier to pass capsules nicknamed palomas, Spanish for dove. The first of the packages, which are about 5ft long, held rehydration tablets and a high-energy glucose gel to help the miners begin to recover their digestive systems. It took an hour for the packages to reach the trapped men.

Rescue teams also sent oxygen down after the miners suggested there was not enough air in the stretches of the mine beneath the cave-in of the main shaft. They plan to include letters as well.

"Can you imagine? After 30 years of marriage we will start sending each other love letters again," said Lilianett Ramírez, whose 63-year-old husband, Mario Gómez is one of the trapped men. Ramírez, who has been waiting at the minehead for nearly three weeks, said: "I want to tell him that I love him so much. I want to tell him that things will be different, that we will have a new life. I will wait as long as I need to see my husband again."

The shelter where the men are trapped, a living-room-sized chamber off one of the mine's lower passages, big enough for all 33 men, is far enough from the landslide to remain intact. The men can also walk around below where the rocks fell. Food will be sent down in several days' time, after the men's stomachs have had time to adjust.

Rescuers sent down questionnaires to determine each man's condition, along with medicine and small microphones to enable them to speak with their families during their long wait.

Sougarret, manager of the state copper giant Codelco's El Teniente mine, said engineers would drill two more shafts. One would be to ensure ventilation and communication in the coming months; another, wider one would bring the miners to surface using a pulley.

Engineers are transporting a more powerful drill from another mine and must decide where to bore the larger hole without risking further cave-ins. Sougarret said it would take three to four months to drill the extraction hole.

The men already have been trapped underground longer than all but a few miners rescued in recent history. Last year, three miners survived 25 days trapped in a flooded mine in southern China, and in 1983 two miners in north-eastern China were rescued after 23 days. Few other rescues have taken more than two weeks.