Explicitly insert the value-1 into the table, then delete the row.

From the SQLite web site:

SQLite keeps track of the largest ROWID that a table has ever held using the special SQLITE_SEQUENCE table. The SQLITE_SEQUENCE table is created and initialized automatically whenever a normal table that contains an AUTOINCREMENT column is created. The content of the SQLITE_SEQUENCE table can be modified using ordinary UPDATE, INSERT, and DELETE statements. But making modifications to this table will likely perturb the AUTOINCREMENT key generation algorithm. Make sure you know what you are doing before you undertake such changes.

I tried this, and it works:

UPDATE SQLITE_SEQUENCE SET seq =<n>WHERE name ='<table>'

Where n+1 is the next ROWID you want and table is the table name.

Could this be dangerous to the integrity of my database?

One way to do it is to insert the first row specifying explicitly the row id you want to start with. SQLite will then insert row ids that are higher than the previous highest.

In solution with SQLITE_SEQUENCE table, the entry into this table seems to be added after the first insert into the table with the autoincrement column is added. In some cases this might cause troubles (i.e autoincrement still starts from 1, not from wanted value).