Did the Buddha intend for everyone to be enlightened?

Was it the Buddha's intention that all beings to be free from suffering i.e. enlightened? > As the Dalai Lama acknowledges , “Buddhism has evolved differently > in different times and places and yet the essential Dharma remains the > same. **The Buddha’s prime concern was that all beings should find > peace and freedom from suffering**. Did he say whether it was possible for everyone to be enlightened, so that there was no one left unenlightened? Would there then be no further (re)birth?