According to figures received by news agency ATS from the Swiss border guards office (EZV) on Monday, 1,321 people entered Switzerland illegally via a border in the canton of Ticino between July 4th and 10th.
Of those, the largest number (665) were Eritrean.
In 996 cases they were sent back over the border, since those who enter the country illegally are not considered as having refugee status.
Those who requested asylum were sent to one of Switzerland's asylum centres for processing.
In total, 14,602 people tried to enter the country illegally in the first four months of 2016, up from 10,362 during the same period last year.
Most of them came through the border with Italy in the canton of Ticino.
The border at Chiasso has long seen high numbers of people attempting to enter Switzerland illegally, and numbers are on the rise.
In late June, the situation led the president of Ticino's government, Norman Gobbi, to call for the border to be shut altogether.
Speaking at the time, Gobbi said other countries including Italy were not properly abiding by the Dublin system, which requires immigrants to be registered at their first point of entry to the Schengen zone, of which Switzerland is a part.
Other cantons are also considering sending border guards to Ticino to help out.
Last week Ticino's border guards made international headlines when an Eritrean immigrant was busted trying to smuggle himself over the border in a suitcase.
Switzerland has around 24,000 Eritreans living in the country (2014 figures), the largest diaspora outside the North African country itself.