The Swiss appear to agree with assisted suicide, but are divided over whether the liberal regulations should apply to patients from abroad.
The surveys come as one of the leading assisted suicide organisations is facing increasing difficulties in finding a permanent home.
Under Swiss law, active euthanasia is illegal but assisted suicide is not. With the latter, the patient has to carry out the final act himself.
According to the polling institute Demoscope, 53 per cent of respondents approved of assisted suicide if a patient is terminally ill.
A further 27 per cent fully agreed with the right to assisted suicide, while 15 per cent came out against.
A similar survey by the Isopublic institute found that 54 per cent of those interviewed would consider assisted suicide for themselves.
About 45 per cent of respondents said they would leave the decision to close friends or relatives in cases where patients are unable to decide for themselves.
Opinions are split over the policy of helping patients from abroad travel to Switzerland to die, notably people from countries where the practice of assisted suicide is banned.
Demoscope said 54 per cent of its respondents opposed "death tourism".
The rival Isopublic survey found regional differences.
While only 46 per cent of the respondents in the German-speaking part came out in favour of such a practice, 56 per cent in the French-speaking regions approved it.
The surveys were carried out among 500 people earlier this month and come amid new controversy about assisted suicide.
The Dignitas organisation – the only group offering help to non-residents – in summer lost the lease on a flat in a Zurich suburb it had used for eight years.
Since then it has moved several times but has so far not been able to find permanent premises.
Other organisations, including the larger Exit, only assist Swiss residents and usually go to them in their own homes.
Justice Minister Christoph Blocher has dismissed calls by the Zurich authorities for a nationwide law aimed at curbing "death tourism". He said existing regulations were sufficient.
Parliament is still to discuss a report on the subject published last year.
swissinfo with agencies
Switzerland has five assisted suicide organisations which help around 350 people each year.
Exit has 50,000 members and helped 150 Swiss people die in 2006.
Dignitas has 5,000 members and helped 195 Swiss and foreigners die in 2006.
ASSISTED SUICIDE IN EUROPE
Switzerland: Assisted suicide and passive euthanasia is legal. Active euthanasia is illegal.
Germany and Italy: Assisted suicide is illegal.
France: Passive euthanasia by doctors or relatives will be legal in future. Active euthanasia remains illegal.
Netherlands and Belgium: permit taking the life of a person who wishes to die.
Britain: has the strictest regulations against assisted suicide in Europe. Many Britons come to Switzerland.