Use RSA keys to derive AES key
With RSA-KEM,* the sender knows a modulus $n$ and a public exponent $e$, and the receiver knows the private exponent $d \equiv e^{-1} \pmod{\phi(n)}$.  To send a message $m$, the sender picks $0 \leq x &lt; n$ uniformly at random, derives $k = H(x)$ for some hash function $H$, computes $y = x^e \bmod n$, and transmits $y$ alongside the authenticated ciphertext $c$ (e.g., AES-GCM) of $m$ under the key $k$.  The receiver recovers $x = y^d \bmod n$, recomputes $k = H(x)$, and recovers $m$ from $c$ using the key $k$.

This protocol is non-interactive in the sense that the sender can package up $(y, c)$ and send it off to the receiver.  There's no authentication of the sender built into the protocol; if you want the receiver to be able to verify which sender sent it, the sender could sign the message $(n, e, y, c)$ giving a signature $s$, and transmit $(y, c, s)$.†

However, like ECIES-KEM, this protocol does not provide a static shared secret between the sender and receiver using their long-term key pairs.  In contrast, in Diffie and Hellman's seminal 1976 public-key cryptosystem, Alice publishes $g^a$ in the telephone book, Bob publishes $g^b$ in the telephone book, and their static shared secret is $g^{ab}$.

This protocol also doesn't provide is deniability—the signature $s$ can be verified by a third party.  In contrast, the Diffie–Hellman public-key cryptosystem does provide deniability because any authenticated ciphertext sent between Alice and Bob under a key derived from their static shared secret $g^{ab}$ could have been created by Alice or Bob: in a symmetric cryptosystem, the power to verify is also the power to forge.



* I would say that this is the RSA analogue of ECIES-KEM, but if anything, I would guess that ECIES-KEM as a concept came after and in response to RSA-KEM as a concept!

† Signing the recipient's key $n$ and $e$ in addition to the ciphertext thwarts Don Davis's misattribution attack on PGP and S/MIME.  If you use the signing key for multiple purposes or contexts, you should make sure to identify the purpose as part of the message you are signing so that a signature used for one purpose can't be abused for an unintended other purpose.  This is sometimes called ‘domain separation’.