Yes, the International Company can hire directly.
Take this example for the understanding; M/s X Co is from ABC country, wants hire 10 people "Y" qualification for the work in ABC country. The,10 people should have valid Passport and Visa shall be arranged by the M/s X Co.
If at all M/s X Co. Wants do business in India needs registration and obtain licensed from our Govt, prior to start of business.